Regression Discontinuinty Designs

The key concept

A threshold in a continuous variable determines treatment assignment

Running variable (or “score”), X: a continuously distributed variable with a clearly defined cutoff (c) that determines which units are assigned to treatment and which ones are assigned to control.

Prior to the treatment, the outcome should not differ between the treatment and control group (continuity assumption). The distribution of the variable which indicates the threshold should have no jumps around this cutoff value.

Example using an arbitrary test score cut-off for being enrolled in tutoring programs on learning outcomes, from Andrew Heiss

Theory

There are two different variants of the RDD:

• sharp RDD: the threshold separates the treatment and control group exactly

• fuzzy RDD: the threshold influences the probability of being treated. this is in fact an instrumental variable approach (estimating a Local Average Treatment Effect [LATE])

The value of the outcome (Y) for individuals just below the threshold is the missing counterfactual outcome. It increases continuously with the cutoff variable, as opposed to the treatment.

Here are some nice elaborations and fifures on these two variants of RDD from the World Bank

Sharp vs Fuzzy RDD illustration from the World Bank

Sharp RDD

"In sharp designs, the probability of treatment changes from 0 to 1 at the cutoff. There are no cross-overs and no non-complance. For example, if a scholarship award is given to all students above a threshold test score of 80%, then the assignment rule defines treatment status deterministically with probabilities of 0 or 1. Thus, the design is sharp.

Fuzzy RDD

In fuzzy designs, the probability of treatment is discontinuous at the cutoff, but not to the degree of a definitive 0 to 1 jump. For example, if food stamp eligibility is given to all households below a certain income, but not all households receive the food stamps, then the assignment rule defines treatment status probabilistically but not perfectly. Thus, the design is fuzzy. The fuzziness may result from imperfect compliance with the law/rule/program; imperfect implementation that treated some non-eligible units or neglected to treat some eligible units; spillover effects; or manipulation of the eligibility index.

A fuzzy design assumes that, in the absence of the assignment rule, some of those who take up the treatment would not have participated in the program. The eligibility index acts as a nudge. The subgroup that participates in a program due to the selection rule is called compliers (see e.g. Angrist and Imbens (1994), and Imbens, Angrist, and Rubin (1996)); under the RDD, the treatment effects are estimated only for the group of compliers."

Advantages of RDD

With an RDD approach some assumptions can be tested. Individuals or units close to the threshold are nearly identical, except for characteristics which are affected by the treatment.

RDD’s strengths include that we can:

• illustrate the design graphically
• test some of the underlying assumptions and support arguments through data visualization
• reliably (unbiased) estimates local average treatment effects
• include relevant confounders in model

Application Demo

Load required packages. In this demo, we will use the package “rdrobust”

install.packages("rdrobust",
                 repos = "http://cran.us.r-project.org")

## 
## The downloaded binary packages are in
##  /var/folders/_c/txgkq4nd3pqfrsyx1ygqk9kh0000gq/T//RtmpKkJ7LF/downloaded_packages

install.packages("rddensity",
                 repos = "http://cran.us.r-project.org")

## 
## The downloaded binary packages are in
##  /var/folders/_c/txgkq4nd3pqfrsyx1ygqk9kh0000gq/T//RtmpKkJ7LF/downloaded_packages

library(tidyverse)  # ggplot(), %>%, mutate(), and friends
# library(broom)  # Convert models to data frames
library(rdrobust)  # For robust nonparametric regression discontinuity
library(rddensity)  # For nonparametric regression discontinuity density tests
library(modelsummary)  # Create side-by-side regression tables

Simple example of applying the rdrobust function

x<-runif(1000,-1,1) # running variable 
y<-5+3*x+2*(x>=0)+rnorm(1000) #outcome with a cut off c at 0 
rdrobust(y,x) #apply rdrobust to view sample output 

## Call: rdrobust
## 
## Number of Obs.                 1000
## BW type                       mserd
## Kernel                   Triangular
## VCE method                       NN
## 
## Number of Obs.                  502          498
## Eff. Number of Obs.             143          144
## Order est. (p)                    1            1
## Order bias  (q)                   2            2
## BW est. (h)                   0.295        0.295
## BW bias (b)                   0.508        0.508
## rho (h/b)                     0.581        0.581
## Unique Obs.                     502          498

Simulate data for demo

Demo Question: fishing mortality on crabs

We are interested in the causal effect of fishing on crab mortality. This question is surprisingly hard to answer because it’s hard to tease apart natural mortality from fishing mortality, but it is an important effect to estimate for fisheries management.

### Make column for observation ID
crab_data <- data.frame(id = seq(1, 1000),
                 
                 ### Add columns for explanatory variables
                 
                 ### Add column for treatment variable
                 fished = c(rep(0, 500), rep(1, 500)),
                 
                 ### Add column for body size
                 size = c(runif(500, min = 10, max = 80),
                          runif(500, min = 60, max = 130)),
                 
                 ### And the rest of the covariates
                 sst = runif(1000, min = 10, max = 16),
                 salinity = runif(1000, min = 1, max = 10),
                 npp = runif(1000, min = 0, max = 1),
                 
                 ### And the error term
                 error = rnorm(1000, mean = 0, sd = 2))

### Visualize
ggplot(crab_data) +
  geom_boxplot(aes(x = size, group = fished)) +
  geom_vline(xintercept = 70)

### center size at legal catch size
crab_data <- crab_data %>%
  mutate(size_centered = size - 70)
  
### Make column for outcome variable (total mortality) 
crab_data <- crab_data %>%
  mutate(natural_mortality = 10 + -0.4*size_centered + 2*sst + 0.3*npp + 1.5*salinity + error,
         fishing_mortality = ifelse(size_centered < 0 & fished == 0, 
                                    10 + -0.1*size_centered,
                                    ifelse(size_centered < 0 & fished == 1,
                                           30 + 0.4*size_centered,
                                           ifelse(size_centered > 0 & fished == 0,
                                                  10 + -0.1*size_centered,
                                                  30 + 0.4*size_centered))),
         total_mortality = natural_mortality + fishing_mortality)

### Visualize mortality outcomes   
ggplot(crab_data) + 
  geom_point(aes(x = size_centered,
                 y = natural_mortality,
                 color = fished))

ggplot(crab_data) + 
  geom_point(aes(x = size_centered,
                 y = fishing_mortality,
                 color = fished))

ggplot(crab_data) +
  geom_point(aes(x = size_centered,
                 y = total_mortality,
                 color = fished))

### Visualize covariates
ggplot(crab_data) +
  geom_point(aes(x = size_centered, 
                 y = sst,
                 color = fished))

ggplot(crab_data) +
  geom_point(aes(x = size_centered, 
                 y = salinity,
                 color = fished))

ggplot(crab_data) +
  geom_point(aes(x = size_centered, 
                 y = npp,
                 color = fished))

Step 1: Determine if process of assigning treatment is rule-based

Example: Rule-based example with cut off: fishing size limits of crabs

In order to be legally harvest, crabs must be larger than 70mm. Crabs smaller than 70mm are not legal to harvest. Harvesting is thus rule-based, according to size. Here, we would probably expect mortality to decline with body size, but the harvest rule changes this relationship at the discontinuity.

Step 2: Determine if the design is fuzzy or sharp

Since we know that the program was applied based on a rule, we next want to figure out how strictly the rule was applied (e.g. was there a lot of illegal harvest of crabs that were too small? Were all crabs over 70mm harvested? ).The threshold was 70 mm for legal harvest — e.g., did people who caught crabs that scored 68 mm slip through cracks? The easiest way to check this is with a graph, and we can get exact numbers to verify with a table.

ggplot(crab_data, aes(x = size_centered, y = fishing_mortality, color = fished)) +
  # Make points small and semi-transparent since there are lots of them
  geom_point(size = 0.5, alpha = 0.5,
             position = position_jitter(width = 0, height = 0.25, seed = 1234)) +
  # Add vertical line
  geom_vline(xintercept = 0) +
  # Add labels
  labs(x = "Size (centered on 70 as cut-off)", y = "Fished or not") +
  # Turn off the color legend, since it's redundant
  guides(color = "none")

This discontinuity looks fuzzy rather than sharp We see some evidence of non-compliance around the size-based harvest rules. We will verify in Step 3.

Comparison of Fuzzy vs Sharp Discontinuities from Causal Inference: The MixTape by Cummingham

Step 3: Check for discontinuity in running variable around cutpoint

We next verify our conclusionss from the above visualization that the design is a fuzzy disconintuinity with a table examinging if there crabs under 70 mm harvested, and some over 70mm that weren’t.

crab_data  %>%
    group_by(fished, size_centered<= 0) %>%
summarize(count = n())

## `summarise()` has grouped output by 'fished'. You can override using the
## `.groups` argument.

## # A tibble: 4 × 3
## # Groups:   fished [2]
##   fished `size_centered <= 0` count
##    <dbl> <lgl>                <int>
## 1      0 FALSE                   82
## 2      0 TRUE                   418
## 3      1 FALSE                  437
## 4      1 TRUE                    63

Based on the table, we can conclude this is a fuzzy design becuase there are some crabs over the cut-off that were not fished, and some under that were fished.

Step 4: Check for discontinuity in outcome across running variable

Next, we need to see if any crabs self selected on either side of the size threshold; this seems unlikely. But, first, we’ll make a histogram of the running variable (size) and see if there are any big jumps around the threshold:

 ggplot(crab_data, aes(x = size_centered, fill = fished)) +
  geom_histogram(binwidth = 2, color = "white", boundary = 0) +
  geom_vline(xintercept = 0) +
 labs(x = "Size", y = "Count", fill = "Legal to fish")

## Warning: The following aesthetics were dropped during statistical transformation: fill
## ℹ This can happen when ggplot fails to infer the correct grouping structure in
##   the data.
## ℹ Did you forget to specify a `group` aesthetic or to convert a numerical
##   variable into a factor?

Here it doesn’t look like there’s a jump around the cutoff. There’s a tiny visible difference between the height of the bars right before and right after the 70-mm sie threshold (centered at 0), but it seems to follow the general shape of the overall distribution.

Step 5: Measure the size of the effect

There’s a fuzzy discontinuity, but how big is it? And is it statistically significant?

Fuzzy RDD as IV

This is likely a fuzzy RDD set up: some crabs < 70mm are probably harvested illegally, and fishers are not catching every crab > 70mm. So the treatment assigned is not necessarily the treatment received. To estimate the effect of fishing on total crab mortality in a fuzzy RDD, we take a two stage least squares approach (using a the fuzzy RDD as an IV.

Recall from Session 12 that instruments let us isolate causal effects for just compliers: they let us find the complier average causal effect, or CACE (the effect of a treatment for subjects/units who comply with the experimental treatment assigned to their sample group).

In this case, the instrument is fairly easy and straightforward: we create a variable that indicates if someone is above or below the threshold. That’s all. This variable essentially measures what should have happened rather than what actually happened.

Surprisingly, it meets all the qualifications of an instrument too:

• Relevance (\(Z \rightarrow X\) and \(\operatorname{Cor}(Z, X) \neq 0\)): The cutoff causes access to fishing of crabs that leads to mortality.
• Exclusion (\(Z \rightarrow X \rightarrow Y\) and \(Z \nrightarrow Y\) and \(\operatorname{Cor}(Z, Y | X) = 0\)): The cutoff causes fishing mortality only through the harvest program.
• Exogeneity (\(U \nrightarrow Z\) and \(\operatorname{Cor}(Z, U) = 0\)): Unobserved confounders between the harvest program and fishing mortality are unrelated to the cutoff, since it may be biologically meaningful but the exact number is somewhat arbitrary.

Analyze fuzzy RDD

First we will create the IV from the cut-off. We have already centered the running variable (size) on 0, so now we just need to create an indicator variable if the size if above or below 0.

##NEED TO FINISHED

size_centered <- crab_data %>%
  mutate(above_cutoff  = size_centered >= 0,
         below_cutoff = size_centered <= 0)
size_centered 

##        id fished      size      sst salinity         npp        error
## 1       1      0  33.37310 10.59927 3.887024 0.494596675 -1.073614790
## 2       2      0  41.41376 14.76165 5.206678 0.492683967  1.842847368
## 3       3      0  51.62351 11.12562 7.973739 0.487321320 -1.150183228
## 4       4      0  39.96777 15.33336 5.004385 0.680442168 -0.767621241
## 5       5      0  38.48896 12.75092 3.002153 0.119928838 -2.464746073
## 6       6      0  54.16535 10.72544 6.811565 0.421503302 -2.056298479
## 7       7      0  74.16030 13.38142 4.489062 0.281738795  0.084957871
## 8       8      0  64.69715 14.61249 2.781528 0.526460395  0.268678090
## 9       9      0  41.80104 13.02843 6.640495 0.294976354  3.320008667
## 10     10      0  19.90219 13.01592 4.135263 0.575951713  0.146680062
## 11     11      0  25.72918 11.94644 1.564524 0.916633083  0.119128951
## 12     12      0  74.17120 13.71824 3.096980 0.973887147 -2.011411746
## 13     13      0  16.39916 15.46050 5.053012 0.204417424 -0.092828793
## 14     14      0  52.13472 15.88613 2.097055 0.584458308  3.469534927
## 15     15      0  27.15036 14.65409 9.476714 0.897742154  2.536128422
## 16     16      0  69.70959 11.44734 3.152656 0.509893499 -0.435135470
## 17     17      0  47.44967 11.37143 3.030767 0.240254555  0.972488359
## 18     18      0  12.94942 13.41042 6.592244 0.971215750 -3.392684813
## 19     19      0  21.08850 15.59445 1.716652 0.827355800  1.473752951
## 20     20      0  43.68907 14.03203 3.104641 0.919271898  2.374906447
## 21     21      0  49.27901 14.69721 5.103537 0.688269655  2.981330814
## 22     22      0  77.20233 10.36719 1.905043 0.402658348 -2.156394649
## 23     23      0  75.82050 10.38967 6.414845 0.751740434  1.754465156
## 24     24      0  37.92843 11.79126 1.028065 0.729490436  2.283081084
## 25     25      0  65.85707 13.73250 2.568082 0.810565792  2.245472442
## 26     26      0  20.73500 15.04458 8.030145 0.305577752  1.305043084
## 27     27      0  75.62863 10.55658 1.641082 0.295610174  2.690527344
## 28     28      0  66.32443 12.35095 3.595475 0.061130400  3.637177230
## 29     29      0  38.71703 15.38567 3.028464 0.466630139  0.681023972
## 30     30      0  19.68255 14.96014 8.759834 0.909825013 -0.316410136
## 31     31      0  44.06650 11.03813 2.116915 0.251121590  4.318064057
## 32     32      0  60.80977 14.58397 9.145512 0.241336541  3.246976808
## 33     33      0  61.13586 12.28360 8.056790 0.351188044 -2.040257663
## 34     34      0  12.37440 13.73760 5.519380 0.746217108 -1.775852977
## 35     35      0  14.05561 15.12592 7.386041 0.674171328 -0.021853185
## 36     36      0  70.77356 13.77019 3.963972 0.127754140 -2.792951737
## 37     37      0  27.09370 14.61036 6.617635 0.774869803  1.339523037
## 38     38      0  29.23035 10.48532 7.256270 0.244572551 -0.377570183
## 39     39      0  63.11804 15.69887 5.395231 0.468912730  1.374590215
## 40     40      0  25.83693 11.82498 3.384566 0.302259645 -1.880109058
## 41     41      0  13.87111 12.27457 8.750711 0.951705037 -2.804488578
## 42     42      0  12.48936 14.07721 4.994538 0.431387697 -0.988109064
## 43     43      0  43.19683 13.39142 5.813704 0.249399324  3.079072235
## 44     44      0  46.59476 11.02856 3.579972 0.413850058  1.109878199
## 45     45      0  16.06293 15.30256 8.724323 0.520869543 -1.304714360
## 46     46      0  64.19618 15.37798 4.880369 0.758276488 -0.547479415
## 47     47      0  66.52012 15.52607 4.803162 0.772996419  1.077692649
## 48     48      0  36.28493 15.18486 7.415118 0.257804012  0.253193271
## 49     49      0  74.23490 10.86472 5.322908 0.698600599  2.164984112
## 50     50      0  67.23035 10.90189 9.523228 0.987741726  4.530373347
## 51     51      0  36.37309 15.37575 9.074279 0.515469426  4.348085366
## 52     52      0  11.92205 11.89925 8.546083 0.354368949  3.070311258
## 53     53      0  71.17861 12.40579 3.648319 0.441485061 -2.150947687
## 54     54      0  23.25916 14.16284 3.263267 0.600542699 -1.776892170
## 55     55      0  51.11880 13.10782 9.560309 0.975718399  0.399962158
## 56     56      0  25.47797 15.74108 2.187035 0.321954943 -3.181568129
## 57     57      0  13.92030 10.88714 7.978228 0.292232560 -0.431999740
## 58     58      0  75.37467 14.80403 9.518592 0.197831195  2.195268021
## 59     59      0  47.92665 14.15736 9.994849 0.866407647  1.024548009
## 60     60      0  12.87387 14.32639 1.436245 0.869400671 -1.255628977
## 61     61      0  31.97767 10.94018 6.969154 0.357436004 -1.284833273
## 62     62      0  64.99726 12.81974 2.756903 0.164609042 -1.532447205
## 63     63      0  46.19775 13.99349 2.522038 0.622985227  1.945550088
## 64     64      0  60.36406 15.95188 5.602029 0.294745947  1.565621091
## 65     65      0  42.11466 15.80957 8.432459 0.813238875 -0.522785163
## 66     66      0  69.07083 14.98427 8.766221 0.283023220  0.004624792
## 67     67      0  12.02701 14.81057 9.922681 0.784318202  0.589750666
## 68     68      0  27.21351 12.16373 2.179820 0.863419081  3.071398308
## 69     69      0  49.43366 13.87355 4.069447 0.511862504 -5.584350659
## 70     70      0  18.61745 15.76411 3.249029 0.650089623 -2.062714285
## 71     71      0  71.88315 11.98593 2.668217 0.177248153  0.520961636
## 72     72      0  73.15826 13.87524 7.766180 0.768716742  0.289615917
## 73     73      0  26.18027 11.72852 6.109876 0.522584254  2.535256856
## 74     74      0  12.26033 14.94655 3.870162 0.990094313 -2.312723554
## 75     75      0  27.73463 15.68789 8.980212 0.479579740 -0.488648754
## 76     76      0  36.69774 14.27316 8.528913 0.750989122 -1.478070010
## 77     77      0  77.83635 14.27551 6.805031 0.659488135  2.339661849
## 78     78      0  66.27114 11.33931 5.085159 0.726599531 -1.732131332
## 79     79      0  20.94700 10.07947 6.996821 0.014302273  0.019519622
## 80     80      0  27.60740 14.30717 8.925224 0.076955062  0.762314449
## 81     81      0  59.86536 12.52449 4.784308 0.770116679  1.025635939
## 82     82      0  14.32249 11.83245 7.345967 0.926316587 -1.775175849
## 83     83      0  57.94736 13.67874 2.100912 0.904102330  0.218773280
## 84     84      0  77.11781 11.63143 8.136935 0.790796537  0.656035849
## 85     85      0  10.13398 12.61578 8.731368 0.764309913  0.342912428
## 86     86      0  36.64132 10.77696 3.587292 0.951976947  1.104377451
## 87     87      0  38.97021 13.46027 9.142175 0.676645987  0.920668512
## 88     88      0  63.24388 14.86026 2.223349 0.378872704  4.164443202
## 89     89      0  37.93457 11.30461 8.641627 0.030429876 -1.044644063
## 90     90      0  28.66860 12.64767 9.682197 0.902427718  0.285185985
## 91     91      0  29.61235 14.53405 8.029733 0.094295227 -4.192061480
## 92     92      0  15.37892 13.48581 4.877622 0.182142639  0.113833825
## 93     93      0  24.65556 13.06647 5.855784 0.792670486  2.231774653
## 94     94      0  60.88257 15.01456 8.832034 0.586692832 -3.496206099
## 95     95      0  43.69759 11.23137 7.986527 0.264909068 -1.359946808
## 96     96      0  17.88836 15.29865 9.914078 0.815960316 -0.643685532
## 97     97      0  65.98527 14.63569 8.735918 0.974536126  1.874956314
## 98     98      0  17.04179 14.32140 2.726958 0.558466529 -0.420152830
## 99     99      0  75.20136 12.28832 8.465133 0.418911049 -3.622802907
## 100   100      0  73.26023 12.55857 3.035576 0.716546475 -0.489421911
## 101   101      0  42.05973 11.98217 2.893860 0.028887988  1.251864277
## 102   102      0  16.53942 11.57621 1.381403 0.758359779  0.208415505
## 103   103      0  25.15308 11.21432 8.773388 0.915596707 -2.033982867
## 104   104      0  44.83964 15.48664 6.312367 0.544482537 -5.643629772
## 105   105      0  46.69616 12.25478 2.701779 0.033052348  1.809515215
## 106   106      0  39.22486 12.98355 9.713968 0.800321290  1.819143909
## 107   107      0  40.76099 12.82462 7.803460 0.540951464 -3.287322085
## 108   108      0  43.75537 13.91665 5.853926 0.815857556 -3.031226804
## 109   109      0  63.09848 15.94103 7.951839 0.486443270 -0.989115730
## 110   110      0  53.83185 11.95210 3.783016 0.143505742 -1.129135480
## 111   111      0  25.94164 15.92858 7.452694 0.612250604 -1.481500784
## 112   112      0  38.91129 12.63588 1.011004 0.624500828 -2.791958189
## 113   113      0  70.66383 10.41061 5.861048 0.071132711  0.264732414
## 114   114      0  54.26053 10.64339 9.629680 0.148267430 -1.266253659
## 115   115      0  77.24640 10.62828 9.773420 0.912052301  2.178884062
## 116   116      0  32.30771 13.45395 1.244513 0.799894103 -1.463932103
## 117   117      0  46.25095 10.22329 2.239068 0.298696314  5.090604858
## 118   118      0  64.68883 10.29096 9.558756 0.341365145 -0.078170343
## 119   119      0  69.23720 13.58166 9.013647 0.211115374 -1.672705385
## 120   120      0  31.81627 15.99567 7.025038 0.816575342  0.764453202
## 121   121      0  47.36487 13.66874 9.055389 0.973902941  0.926559968
## 122   122      0  71.86791 11.85501 3.038448 0.266165299 -1.594563186
## 123   123      0  26.76832 12.21446 4.888050 0.294325066 -0.749292791
## 124   124      0  58.95658 15.02226 4.056528 0.040936453  2.480414991
## 125   125      0  60.03132 11.77063 6.940378 0.852810399 -1.059344630
## 126   126      0  13.95451 11.62312 2.154888 0.565934502  1.889018113
## 127   127      0  28.84147 11.09523 4.123034 0.314001128  0.348941195
## 128   128      0  55.75212 15.55009 5.938676 0.979489752  1.042588444
## 129   129      0  46.83145 11.27260 4.468514 0.828551237 -1.274033141
## 130   130      0  24.40523 14.41496 6.835154 0.945057308  2.470234709
## 131   131      0  51.66827 10.54242 3.225351 0.806369240  0.955288778
## 132   132      0  16.95237 15.87858 8.397524 0.564503106  0.632548429
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## 189   189      0  11.70622 15.37385 1.806424 0.625180312  1.419522858
## 190   190      0  56.92235 10.00408 4.825135 0.338130000  0.713367927
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## 204   204      0  15.72896 12.43392 3.769447 0.160212963  0.167652177
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## 211   211      0  21.56700 12.48634 6.391390 0.659591349  3.246506984
## 212   212      0  26.64370 15.91677 3.441875 0.823806694  0.263306993
## 213   213      0  48.67881 11.26490 4.486115 0.412615071 -0.430131381
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## 219   219      0  29.96744 13.88616 6.270915 0.626851060  0.465497352
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## 221   221      0  40.00163 11.92891 3.140213 0.213127193  1.220706651
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## 223   223      0  77.90757 15.32256 8.732507 0.501020048  2.970636633
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## 228   228      0  38.73624 10.27145 9.340725 0.271584277  1.613474583
## 229   229      0  24.85324 14.50066 1.197655 0.953933537  1.462021969
## 230   230      0  43.43103 14.50792 7.725480 0.165115024  2.393059727
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## 235   235      0  66.54842 11.60874 2.389795 0.070607719  2.843552051
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## 250   250      0  26.55932 11.29264 5.662438 0.904877696  1.782028628
## 251   251      0  55.75768 14.82242 6.285836 0.437849965  0.169624828
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## 254   254      0  52.60212 11.62509 8.050945 0.816747312  0.168460509
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## 257   257      0  45.44774 10.46914 5.063449 0.408129274  1.249826581
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## 282   282      0  49.58939 15.54253 3.942430 0.228934414  1.950163200
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## 308   308      0  72.90273 10.00525 3.220888 0.251615859  3.702163957
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## 312   312      0  79.80301 12.29750 7.400945 0.069610425  3.437474296
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## 317   317      0  14.57563 10.65990 7.506856 0.239255951  2.193858999
## 318   318      0  20.99038 14.49182 8.482911 0.984806948 -0.319214728
## 319   319      0  30.29986 15.78368 2.547947 0.334053014 -2.862390849
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## 329   329      0  40.33636 15.08978 9.550083 0.591600812  2.773493537
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## 331   331      0  41.54062 13.85169 2.221575 0.067522590 -4.662877952
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## 334   334      0  46.05285 14.68161 1.297102 0.501943247 -3.561793893
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## 339   339      0  64.80772 12.61406 5.601512 0.416484439 -1.678711093
## 340   340      0  66.57977 12.27946 4.282340 0.599660745  2.069628838
## 341   341      0  48.21908 10.36068 6.834804 0.743605861  1.306284478
## 342   342      0  56.16547 11.12928 2.209245 0.039999695  0.470887061
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## 344   344      0  41.10567 14.60525 4.511541 0.430584218 -2.797730076
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## 347   347      0  66.91505 11.97937 1.377518 0.854329573  1.664594046
## 348   348      0  45.31870 14.13358 7.139068 0.084470250 -3.064708587
## 349   349      0  11.02316 12.82651 8.865534 0.770503413 -1.297047510
## 350   350      0  40.90840 15.05980 3.887900 0.027562850 -0.742123952
## 351   351      0  61.73969 15.56404 2.309854 0.722906907  0.779341442
## 352   352      0  31.02340 10.00324 9.187531 0.360918917  1.635017942
## 353   353      0  62.30343 12.32077 2.048490 0.357509851  3.201057784
## 354   354      0  62.35872 13.72809 8.885294 0.624784651  0.237643237
## 355   355      0  15.79277 14.96551 4.338136 0.812201337 -1.071790665
## 356   356      0  28.32050 11.64002 8.501668 0.195537815 -2.559917259
## 357   357      0  12.80881 13.50887 7.068706 0.596623966 -0.873846230
## 358   358      0  18.68231 10.67802 6.598852 0.498026164 -0.055879885
## 359   359      0  61.87716 11.63985 8.907720 0.120424772  2.786273806
## 360   360      0  45.77652 11.46294 4.198947 0.593324346  1.006053972
## 361   361      0  24.39431 14.83260 6.413530 0.438778059  3.101302682
## 362   362      0  24.36346 10.73254 9.700002 0.623549878 -1.788450409
## 363   363      0  25.50300 13.53461 8.286810 0.627634437 -0.134290009
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## 366   366      0  22.62083 10.08567 3.861635 0.346635636  1.224793953
## 367   367      0  27.91125 11.96933 2.134880 0.143564355 -3.106608729
## 368   368      0  30.99211 11.87581 4.674868 0.325149701  0.757626991
## 369   369      0  64.30438 11.93617 6.296815 0.100725546 -4.379288479
## 370   370      0  67.75398 15.39552 7.124523 0.021317158  1.328038911
## 371   371      0  74.84444 14.42319 2.332006 0.261976593  0.703190840
## 372   372      0  60.36838 10.42344 5.934303 0.094930030  1.374463250
## 373   373      0  55.53085 11.52427 9.100810 0.183179804 -3.578914585
## 374   374      0  27.17614 12.54802 9.081595 0.977158589  3.694738067
## 375   375      0  79.76175 13.97977 3.484129 0.631162328 -3.155881000
## 376   376      0  66.44929 14.34790 1.978717 0.043292703 -0.430024966
## 377   377      0  38.93744 13.23568 1.791522 0.322480845  0.448590692
## 378   378      0  35.66485 11.59185 7.672887 0.114719687 -1.855558729
## 379   379      0  38.29131 12.21905 5.176548 0.384148553  0.090364581
## 380   380      0  14.93573 15.69266 8.422685 0.038092417 -2.727505531
## 381   381      0  60.02705 12.35447 9.011425 0.531412574  0.438808910
## 382   382      0  55.80625 11.09505 9.746703 0.357942035  0.984272181
## 383   383      0  42.23635 12.60649 9.256905 0.609194689 -0.309585652
## 384   384      0  61.61325 12.66639 1.428402 0.122823809  1.587781962
## 385   385      0  36.54355 12.17845 7.146418 0.466838249  2.155721388
## 386   386      0  45.66845 12.62271 7.468700 0.231174840  3.041112312
## 387   387      0  75.43449 13.80491 3.169636 0.988880865 -4.265641899
## 388   388      0  57.97498 14.00407 5.439856 0.183497970  2.389069640
## 389   389      0  16.58439 12.12109 6.904335 0.004592668 -1.695159481
## 390   390      0  29.34349 11.52012 8.876113 0.206136626 -0.826494335
## 391   391      0  59.93914 12.72481 8.960705 0.574374454 -4.641294329
## 392   392      0  49.34955 12.91799 6.009359 0.156798044  0.624775697
## 393   393      0  40.71054 15.39895 7.575792 0.785529592  2.786752591
## 394   394      0  31.02149 14.39653 7.627913 0.188225026  2.881158349
## 395   395      0  25.72459 11.52970 1.677692 0.599573665 -0.402266772
## 396   396      0  79.01091 13.64082 3.918149 0.949652760 -0.371671492
## 397   397      0  20.52129 12.15753 2.105225 0.883754080  2.193449220
## 398   398      0  16.10429 14.71220 4.036390 0.726904152  0.704144278
## 399   399      0  66.19587 15.11398 6.322207 0.764371166 -1.086724303
## 400   400      0  30.14803 12.05470 2.322738 0.049622783 -3.208141917
## 401   401      0  48.64880 13.93406 8.960797 0.471114014  1.644699670
## 402   402      0  74.18884 14.42333 9.670613 0.209059123 -1.747673955
## 403   403      0  77.28147 10.23882 3.209177 0.996699156  2.321923528
## 404   404      0  73.64180 11.67407 1.888203 0.115296102  1.710142250
## 405   405      0  28.47692 15.40512 8.883600 0.215135565 -1.405606806
## 406   406      0  50.89501 11.00258 5.011919 0.057418960  1.204107078
## 407   407      0  20.30261 13.61400 3.246284 0.388872994  0.766705856
## 408   408      0  13.13903 14.22943 1.080510 0.336790988  1.745946131
## 409   409      0  51.64684 14.63265 8.798376 0.737869869  2.512492402
## 410   410      0  53.55931 14.73616 9.878112 0.010183791 -1.091658800
## 411   411      0  32.54231 13.64795 6.375715 0.765458696 -2.376192388
## 412   412      0  54.74182 13.00167 8.312435 0.748293975 -2.499717409
## 413   413      0  40.41622 11.52543 1.589100 0.473813273  0.705646348
## 414   414      0  52.81326 10.22180 6.624250 0.276103804  0.146287143
## 415   415      0  26.47039 14.51979 5.416370 0.940606884  0.959106255
## 416   416      0  39.38440 10.35643 1.212599 0.925908485  0.659348134
## 417   417      0  46.02137 10.07010 3.622698 0.648214367  1.074051446
## 418   418      0  20.92300 12.09343 3.787904 0.948616337  4.325867051
## 419   419      0  29.10737 14.91165 8.477723 0.558333712  0.384311133
## 420   420      0  61.89565 14.57820 2.482310 0.850618929 -1.774537372
## 421   421      0  62.95618 13.66329 6.384703 0.558570524  3.901671010
## 422   422      0  70.04591 11.92358 7.041287 0.651439219 -0.637115170
## 423   423      0  63.28079 13.30145 4.668653 0.174675365 -1.611973173
## 424   424      0  79.96402 10.37368 5.031956 0.078792606  0.430637560
## 425   425      0  43.38596 15.02212 3.179875 0.549459375 -2.364912352
## 426   426      0  15.28933 10.83186 6.667563 0.468603011 -0.185929581
## 427   427      0  40.72771 15.40827 2.671683 0.732077773 -1.843659660
## 428   428      0  34.64193 10.78302 9.537024 0.607795965 -0.219501015
## 429   429      0  60.71692 12.91494 4.008034 0.114555355  3.359991740
## 430   430      0  64.72333 13.69236 1.027972 0.301706112  0.269325901
## 431   431      0  79.13657 10.44787 5.591979 0.345200806 -2.398388658
## 432   432      0  79.51190 13.24166 2.050861 0.881751652  0.233378236
## 433   433      0  78.91863 12.52914 3.904363 0.423076503 -1.443674942
## 434   434      0  44.44442 12.58140 2.306337 0.356661385  0.193100685
## 435   435      0  58.00912 11.93226 3.704987 0.960284182 -4.913095040
## 436   436      0  25.23223 13.76184 4.237650 0.843008434 -0.024266489
## 437   437      0  39.35843 10.59202 6.314168 0.069633855  2.516814691
## 438   438      0  75.24296 11.57476 8.410532 0.705017806  0.084102223
## 439   439      0  27.71826 15.27168 3.156523 0.991856595 -2.493728337
## 440   440      0  77.22175 12.61479 4.801405 0.468704649  3.656407070
## 441   441      0  68.00547 11.32797 5.707440 0.232078453  1.071899179
## 442   442      0  21.69133 10.14345 2.903833 0.777419007  3.068916317
## 443   443      0  22.09856 15.06121 2.748912 0.974392610  1.869526910
## 444   444      0  17.28946 13.51993 6.485765 0.593751166  0.229774947
## 445   445      0  51.56032 15.28846 1.815659 0.698202156  3.864731822
## 446   446      0  30.56757 10.48010 2.671005 0.271645685  1.054050303
## 447   447      0  35.74800 12.86075 9.352652 0.065908138 -1.167452722
## 448   448      0  18.56012 12.25494 5.663800 0.804115437 -1.116673997
## 449   449      0  45.07920 13.63505 1.469759 0.149348758 -0.562335853
## 450   450      0  75.34443 13.05212 8.924711 0.118687865 -1.821327424
## 451   451      0  55.93422 13.19786 8.018309 0.619074552 -5.578428216
## 452   452      0  47.12225 15.37706 4.445255 0.567603333 -0.698005172
## 453   453      0  10.07339 12.83912 6.382477 0.068685685 -2.050503140
## 454   454      0  41.09557 10.66078 9.783400 0.571956698  1.645759030
## 455   455      0  52.91695 13.03602 9.642042 0.419087881  0.740359177
## 456   456      0  78.31311 15.40721 3.709094 0.570784008  1.465872538
## 457   457      0  52.62335 10.74554 9.189306 0.437095043  0.016387802
## 458   458      0  72.42658 10.88964 7.646019 0.117650913 -4.610150051
## 459   459      0  41.27513 12.68254 8.891114 0.552324052  1.796510054
## 460   460      0  28.93096 11.11435 9.001809 0.900962865  2.716604656
## 461   461      0  60.53190 15.99563 8.394791 0.902134400  1.363844593
## 462   462      0  56.59868 15.82920 6.477396 0.763885150  1.642970888
## 463   463      0  73.50876 14.23739 3.684920 0.688357751  0.454739817
## 464   464      0  49.12118 12.38653 2.011254 0.511876340  0.116387081
## 465   465      0  64.76135 12.00728 3.193714 0.582948487  1.834576541
## 466   466      0  24.86429 13.07956 7.080961 0.700579189  0.090016493
## 467   467      0  12.27289 13.91044 8.092113 0.599398965 -0.322413776
## 468   468      0  57.35645 12.55221 1.117343 0.412707972  2.263467593
## 469   469      0  24.39311 14.69806 3.962089 0.892409819  1.438353770
## 470   470      0  54.43531 11.41509 9.663549 0.186208201 -4.863209631
## 471   471      0  48.09537 13.77448 2.697798 0.820922712  0.434813743
## 472   472      0  12.01373 14.33048 5.441673 0.785917595  2.605085344
## 473   473      0  77.01277 15.76601 6.158280 0.753946979 -0.927764727
## 474   474      0  10.62894 10.39360 9.384675 0.846822963 -2.055509548
## 475   475      0  30.21185 15.23776 9.488815 0.352104198  0.535589579
## 476   476      0  47.09577 11.42589 3.994019 0.859347369  2.956419587
## 477   477      0  33.37782 14.86671 3.397280 0.415468908  2.150559478
## 478   478      0  54.76141 13.84148 6.660449 0.959526783 -0.505611292
## 479   479      0  38.48097 15.17031 5.560408 0.300289541 -0.486370795
## 480   480      0  21.71850 12.50159 9.884203 0.381214523  2.661085023
## 481   481      0  44.76446 10.80835 2.491507 0.189111282 -2.227285766
## 482   482      0  78.85632 12.94730 4.128994 0.450103302  1.358801349
## 483   483      0  12.45272 11.86493 9.149346 0.024618509  0.199235901
## 484   484      0  41.54095 14.20670 7.517626 0.168632520  2.440411224
## 485   485      0  72.02149 11.63221 4.584868 0.855832749 -2.413333458
## 486   486      0  73.99236 11.09845 8.177046 0.637962416 -1.625941057
## 487   487      0  32.00560 13.15439 4.936094 0.813396239 -3.914097369
## 488   488      0  47.53722 11.77040 1.492048 0.591462354 -0.985854395
## 489   489      0  13.67741 12.50723 5.370721 0.331698807  2.769196835
## 490   490      0  21.03165 13.24397 2.484302 0.534633218  1.097118106
## 491   491      0  24.88361 11.38887 7.692265 0.428352930  0.584143113
## 492   492      0  46.74800 10.39002 7.521643 0.492999859  0.601150877
## 493   493      0  74.06624 12.62446 4.453065 0.393895330  2.805989602
## 494   494      0  78.86219 13.02513 4.766772 0.566620105 -3.118752671
## 495   495      0  51.67231 12.00818 8.718667 0.820933729  3.933927062
## 496   496      0  75.47612 11.62463 8.586977 0.925791845 -2.065576918
## 497   497      0  16.01227 11.45565 1.636149 0.328830353 -1.045087670
## 498   498      0  26.61077 13.49038 9.418296 0.445244231  0.437028301
## 499   499      0  79.30805 14.24209 2.974569 0.640624065 -2.192106166
## 500   500      0  65.99257 14.01162 8.658432 0.650782300 -2.395892566
## 501   501      1 128.66180 10.72696 9.842567 0.733573247  1.958298245
## 502   502      1 118.93565 12.54715 5.410028 0.558840320 -1.176928284
## 503   503      1  81.17555 10.06840 7.058892 0.530795175 -3.090019697
## 504   504      1 116.49117 11.99777 8.312494 0.421241399 -1.043119003
## 505   505      1 120.40721 11.26685 8.789099 0.190276575 -1.097638284
## 506   506      1 124.44620 12.11541 2.690736 0.251705760  0.327654239
## 507   507      1  86.30819 15.33343 1.084810 0.779715861  2.012306613
## 508   508      1  62.86647 14.86820 3.493950 0.088785803  0.924235662
## 509   509      1 125.61412 15.91995 1.803818 0.965712849 -1.659520335
## 510   510      1 127.66988 13.28833 9.464334 0.536303572  0.436965973
## 511   511      1 100.48511 15.45639 8.177680 0.961915815  0.826346850
## 512   512      1  75.36811 14.30498 8.412155 0.356352651 -0.256439963
## 513   513      1  71.39705 15.57216 1.519986 0.148133726 -1.434952820
## 514   514      1  67.54737 11.50367 9.207564 0.004068035  0.446973439
## 515   515      1  71.24889 15.88482 6.028969 0.273149203  2.055073565
## 516   516      1  78.29066 10.17189 3.263527 0.990995826  1.394537006
## 517   517      1  91.07768 10.54245 9.475874 0.098906163 -2.428855047
## 518   518      1  62.55569 10.13990 5.413076 0.190727073 -0.288624848
## 519   519      1  60.77968 10.89944 6.961769 0.338054156  1.707642799
## 520   520      1  73.21243 13.12869 9.325264 0.525336310  0.970150572
## 521   521      1  88.71964 10.96239 9.995992 0.955344328 -0.866013689
## 522   522      1  81.73142 12.52408 1.479711 0.561156171 -5.029804220
## 523   523      1 108.55083 12.74002 4.029586 0.375264286 -0.378969505
## 524   524      1  99.13282 14.62927 7.985373 0.421398927  1.364618162
## 525   525      1  94.94423 12.15862 2.176556 0.835268881  0.854050986
## 526   526      1  91.60096 14.73898 5.382285 0.706959961  1.884640731
## 527   527      1 110.37984 15.13820 6.026520 0.931825949 -2.082300174
## 528   528      1  66.28789 13.32718 8.722159 0.905808832 -0.655171984
## 529   529      1 122.05559 13.63346 5.881148 0.632011099  1.569003840
## 530   530      1 101.88432 15.08065 8.859807 0.558488472 -2.211460514
## 531   531      1 107.63785 13.20073 3.538977 0.320380337 -3.627886013
## 532   532      1  82.61459 14.10887 1.868199 0.129742371  2.882490492
## 533   533      1 103.36896 14.16292 4.920868 0.688582694  0.840716809
## 534   534      1  70.77348 14.40748 1.300076 0.678891051 -1.180857252
## 535   535      1  68.18001 11.38390 9.189775 0.956523859 -0.551879558
## 536   536      1  81.24211 12.70323 8.040088 0.538861470  0.216789107
## 537   537      1 117.15666 12.06597 9.451935 0.565930062  2.985341377
## 538   538      1  84.67316 14.60338 6.103469 0.178594198  3.342425164
## 539   539      1  86.73614 14.22652 4.217756 0.783192700  0.218142948
## 540   540      1  82.91437 12.12173 6.775294 0.198808310  3.026433443
## 541   541      1 124.51124 13.77259 4.309386 0.667265926 -1.243277288
## 542   542      1 125.70890 13.99376 2.763948 0.187139824  1.120823373
## 543   543      1  88.47141 15.23287 3.828099 0.597400467  0.063777948
## 544   544      1 123.10259 14.68605 7.697304 0.279623081 -1.208862613
## 545   545      1 108.77238 12.96582 2.400486 0.377032092 -0.292298341
## 546   546      1  60.36301 11.14860 8.828921 0.872471569 -2.777232136
## 547   547      1  73.41887 13.19359 4.073165 0.387847248 -1.265981666
## 548   548      1  96.32505 14.56277 3.779774 0.633885217  2.868389223
## 549   549      1  80.48531 10.74353 3.192251 0.100182238 -4.038415103
## 550   550      1 116.28010 14.26585 3.141220 0.532891773  0.890445084
## 551   551      1  60.16560 13.57571 2.028837 0.355560557 -0.631199106
## 552   552      1  99.53252 10.06401 9.923850 0.464448719  0.755717967
## 553   553      1  63.28620 13.22484 2.183159 0.307152933  3.447417305
## 554   554      1  75.30975 15.12309 5.996634 0.216659255  2.516900424
## 555   555      1 116.16915 10.77872 1.161179 0.130715740 -2.564956169
## 556   556      1  88.63016 10.92521 7.618076 0.491400612 -0.152639219
## 557   557      1  70.08382 13.43456 7.519779 0.740693916 -3.628030131
## 558   558      1  61.41746 10.91389 6.844805 0.721925867  0.885973240
## 559   559      1 109.50240 10.96977 7.644455 0.057342862  0.469475304
## 560   560      1  68.38059 10.33977 2.077131 0.699653230  1.279405953
## 561   561      1 111.00728 10.36981 6.218477 0.809031210  0.645315698
## 562   562      1 104.42993 15.57706 1.273702 0.070940701 -2.895014077
## 563   563      1 108.73660 14.86551 7.662295 0.691943090  0.240150656
## 564   564      1  91.50070 10.08357 2.333113 0.856674199 -0.063268636
## 565   565      1 110.60263 12.07608 5.739710 0.787290401  5.035617933
## 566   566      1  71.52434 13.01305 4.668341 0.511854753  0.212648481
## 567   567      1  84.76217 10.05980 2.257730 0.919901961 -2.963364288
## 568   568      1  72.82258 12.34789 5.009760 0.566551746  2.496867696
## 569   569      1  85.79820 10.79575 2.863581 0.746567932 -1.950036910
## 570   570      1  88.19628 10.99241 9.516537 0.801336104 -2.764405890
## 571   571      1  96.64884 11.95994 9.729980 0.478648720  1.359728280
## 572   572      1  72.98790 10.16519 3.360097 0.369962405  0.740085020
## 573   573      1  86.87392 11.56993 1.064414 0.725716817  0.806357599
## 574   574      1  72.69397 10.13630 4.276559 0.183189944  2.742726491
## 575   575      1 128.66095 11.95749 3.366398 0.042136591 -3.167278778
## 576   576      1  69.49875 10.86528 6.310217 0.269993082 -1.002418940
## 577   577      1 111.60246 14.39537 2.529886 0.009589370  0.650333932
## 578   578      1  84.29782 13.09225 4.739717 0.850706898  2.397808026
## 579   579      1 103.99697 11.47010 5.840125 0.574324733 -1.359766516
## 580   580      1 100.14833 11.07764 8.859306 0.317493263  0.240592984
## 581   581      1  86.82977 13.17446 8.267386 0.613536613  3.457011322
## 582   582      1  83.80937 12.09852 8.289586 0.026975339  1.994759478
## 583   583      1 107.42773 15.14236 1.183422 0.465367281 -2.718692078
## 584   584      1 105.23397 15.29779 7.669630 0.308770873  0.991494857
## 585   585      1 124.66997 14.28340 7.613566 0.115860842 -3.110150036
## 586   586      1  70.51214 13.22146 4.183743 0.687451377  0.734998131
## 587   587      1 125.60664 13.96650 3.786244 0.920541531 -0.343766905
## 588   588      1  67.00069 10.23857 4.556896 0.385836244  1.890027910
## 589   589      1 129.13688 12.73888 6.067275 0.712776668 -4.194843772
## 590   590      1 114.81607 13.55735 8.181829 0.849765031 -0.005307291
## 591   591      1 100.10045 14.41665 6.455192 0.900119539 -3.740992238
## 592   592      1 102.66591 11.63706 1.274246 0.029162220 -2.898881462
## 593   593      1 122.99356 12.13196 1.101764 0.727489650 -1.993138780
## 594   594      1  77.21096 10.52368 5.085496 0.242091433  4.764579017
## 595   595      1 101.72846 11.44871 9.913190 0.478179386  3.529547502
## 596   596      1 101.61945 10.91539 3.368673 0.520216604  2.854333047
## 597   597      1  64.85063 10.07019 5.270962 0.105249825  0.670770606
## 598   598      1 122.76171 12.04010 4.640172 0.424886371 -2.561575948
## 599   599      1 105.66687 15.14478 5.674720 0.247573998 -2.417037822
## 600   600      1 121.55837 15.76453 3.838335 0.876601125  4.319802429
## 601   601      1 112.94723 11.26197 9.339986 0.335283186  1.143127941
## 602   602      1 108.78830 15.95872 8.944861 0.817788030 -1.433041168
## 603   603      1 116.37886 15.35213 1.661092 0.534897401 -1.763805281
## 604   604      1  68.11584 13.22075 1.509737 0.370609576 -1.987583699
## 605   605      1 115.81458 14.96221 3.205955 0.853914504  0.782482970
## 606   606      1 108.80276 12.61829 3.534472 0.584453374 -2.079368269
## 607   607      1 124.31232 14.09674 5.495373 0.874131650  1.242205911
## 608   608      1 100.47890 11.85367 3.709567 0.848970144 -0.785055016
## 609   609      1  84.79292 12.66472 4.245025 0.210742827 -2.371520048
## 610   610      1  94.80674 14.12869 4.682103 0.196270232 -1.254908821
## 611   611      1 119.10902 12.35150 6.882350 0.076619409 -5.312176280
## 612   612      1 128.39880 12.11254 8.287847 0.388382067  1.495863491
## 613   613      1  91.75451 14.22582 2.428875 0.046452277 -0.712180103
## 614   614      1 128.10039 10.08225 5.597498 0.536057666  0.742354880
## 615   615      1  79.93781 12.85491 4.187477 0.919255650 -0.690143010
## 616   616      1  89.67583 15.15384 9.199450 0.366083281 -2.179853178
## 617   617      1  66.98902 13.83889 5.760551 0.727089552 -1.783532199
## 618   618      1  96.27759 13.97159 7.148535 0.572790738  0.470385544
## 619   619      1  99.27359 10.84785 5.337492 0.219980547 -3.813725218
## 620   620      1  83.31696 11.34227 9.585524 0.016572248  0.329368037
## 621   621      1 100.70485 13.53785 9.016187 0.578994814 -1.905807995
## 622   622      1  79.63926 14.54802 7.342615 0.012052615 -1.445019587
## 623   623      1  60.00277 14.87725 4.646124 0.672086125 -0.124133664
## 624   624      1 117.00113 15.51806 6.880422 0.425578709 -3.119592867
## 625   625      1 105.69794 15.33323 2.506968 0.344894752  0.018806660
## 626   626      1  67.73854 12.43904 2.800202 0.841028990 -0.076868162
## 627   627      1  86.29111 14.23502 9.810102 0.133001855 -1.337569948
## 628   628      1  76.85333 13.47702 2.225704 0.551047304  1.648833208
## 629   629      1 117.46922 13.51376 3.711961 0.232871626 -0.495534112
## 630   630      1  68.86402 11.23073 4.914586 0.940665438 -1.364409813
## 631   631      1 102.49750 10.39358 6.563876 0.464597968  0.912590618
## 632   632      1 120.54398 11.80226 6.003960 0.714310799 -0.500188497
## 633   633      1 125.11897 14.30381 7.497211 0.444596667  0.212362509
## 634   634      1 124.37002 12.92563 2.247579 0.702001183  0.089519874
## 635   635      1 113.44261 11.01468 6.888443 0.660722377  3.204415977
## 636   636      1  91.35938 10.29751 4.031388 0.052484121  2.321986302
## 637   637      1 100.94469 13.81946 3.876487 0.242204686  1.786820992
## 638   638      1  88.44689 11.82081 7.721175 0.875468428 -3.597235446
## 639   639      1  73.60690 14.12891 2.934396 0.834615117  3.949500448
## 640   640      1  68.98993 13.17763 3.801556 0.942990531 -1.055318197
## 641   641      1  71.37233 12.82062 6.614387 0.501353964 -1.493319310
## 642   642      1  97.75019 12.51039 3.995718 0.523871491  1.301660023
## 643   643      1 122.41532 15.43364 6.622390 0.618626134 -0.040323685
## 644   644      1  70.93849 15.81032 1.419149 0.276575797 -0.522207233
## 645   645      1  87.83394 14.98761 5.109594 0.502326638 -1.024051614
## 646   646      1  95.53466 14.44939 9.959573 0.729360538  0.252474281
## 647   647      1 114.92468 15.87622 6.743346 0.909974701 -0.227032148
## 648   648      1 120.51747 15.05331 9.510691 0.764865327 -0.117811617
## 649   649      1  67.05864 12.96700 7.712338 0.367396888  3.199803997
## 650   650      1  64.30626 13.32602 2.196035 0.874782466  0.430597766
## 651   651      1  78.56548 14.63165 1.933291 0.363951449  0.645390277
## 652   652      1  95.52571 13.99748 6.812210 0.290355034  2.444122091
## 653   653      1 107.18505 14.94035 2.026314 0.320897220  0.031706245
## 654   654      1 119.37508 15.35792 3.900137 0.680569881 -3.058047611
## 655   655      1  80.52082 13.91578 2.467172 0.650990049 -0.464629300
## 656   656      1  88.85331 14.99600 2.439910 0.471730644  1.799926499
## 657   657      1  94.61190 15.69955 2.133365 0.831765355 -2.773268668
## 658   658      1 106.67111 14.78894 6.916448 0.970336368 -0.153340925
## 659   659      1 120.04675 13.66810 1.025630 0.789545402 -0.063172595
## 660   660      1  82.29287 11.90016 2.363340 0.534084493  2.094907938
## 661   661      1 124.70957 14.92101 6.247593 0.810891195  0.719090229
## 662   662      1 125.22779 15.59045 2.555901 0.992043210  3.609473695
## 663   663      1 122.86684 13.47476 2.937177 0.006240772 -1.649145972
## 664   664      1 107.67335 11.36824 3.631177 0.983962921  1.117340726
## 665   665      1  66.40335 13.98975 5.651022 0.833072336  1.539870690
## 666   666      1  83.17587 12.21274 3.810252 0.559758361 -1.309890835
## 667   667      1 112.32418 11.53442 6.897642 0.855965885  0.455295365
## 668   668      1  97.59599 10.98855 7.152317 0.877397053  0.982601655
## 669   669      1 113.72329 15.75511 8.068329 0.913725962  0.574179553
## 670   670      1  83.57573 15.13423 6.396247 0.417780723 -2.924459911
## 671   671      1 102.18222 13.04768 7.747705 0.048217680  3.427025008
## 672   672      1 124.83629 15.62546 1.714748 0.394369852 -2.246730066
## 673   673      1 106.81785 10.38022 1.962464 0.526423587  3.755968618
## 674   674      1 111.71839 11.32421 7.426853 0.768984383 -1.332684511
## 675   675      1  79.97339 10.72129 4.072383 0.886890683  3.186964185
## 676   676      1  65.38329 10.43893 5.413427 0.596512839 -3.001085667
## 677   677      1  98.55359 13.81223 8.275291 0.964907162 -2.755431076
## 678   678      1  90.04046 11.76640 3.456765 0.190046407  0.796872471
## 679   679      1  76.78105 14.02580 6.090795 0.021604648 -0.359324758
## 680   680      1  96.73795 11.07538 7.442501 0.220073558  0.392551750
## 681   681      1  62.91359 10.93923 2.413478 0.952720864 -1.969367397
## 682   682      1  80.64682 10.72109 3.925102 0.075342448 -0.664207236
## 683   683      1  70.74408 14.09089 7.029395 0.372088801  0.976304301
## 684   684      1 124.65688 10.13219 9.359171 0.846338860  0.321682448
## 685   685      1  65.63758 15.61733 1.900761 0.630872838 -2.430095385
## 686   686      1 129.53668 11.23610 7.916057 0.786878324 -0.930372039
## 687   687      1  60.86914 10.79154 5.259413 0.897190825 -2.073781573
## 688   688      1  72.65489 15.69691 3.645109 0.181268512  1.494743796
## 689   689      1 125.84247 13.61361 8.676099 0.449239363  1.434543581
## 690   690      1  72.61221 14.86969 8.070578 0.438139186  0.094248311
## 691   691      1 111.90388 11.54071 5.020170 0.489539095 -4.324966063
## 692   692      1  94.17229 10.23505 8.133582 0.135543143 -2.132981754
## 693   693      1  87.11912 13.53680 8.867806 0.889156068 -2.128366891
## 694   694      1  60.49925 11.74020 1.162716 0.409748563 -0.894567881
## 695   695      1 109.08996 12.09353 3.285278 0.064680084 -0.463733146
## 696   696      1 116.03308 13.95364 3.081476 0.700857568  0.946343576
## 697   697      1  69.99515 13.53543 7.706756 0.190040248 -1.251637646
## 698   698      1 120.86060 15.01059 3.227621 0.986207147 -2.186969202
## 699   699      1  91.74006 14.81395 9.193238 0.788563289 -0.755242928
## 700   700      1  97.76639 12.54797 5.700118 0.404303331  0.055526762
## 701   701      1  75.84982 14.85137 2.248547 0.577132475 -2.499587244
## 702   702      1  93.59963 13.98422 6.451097 0.620164218 -2.934682712
## 703   703      1  66.76562 15.53498 1.555949 0.170714606  2.493795487
## 704   704      1  77.26716 13.53868 5.305663 0.236936145 -0.612275691
## 705   705      1 128.68622 13.77983 5.789284 0.943035304 -1.312156147
## 706   706      1  73.61578 12.62189 3.768309 0.537431362  1.465631383
## 707   707      1 124.18422 13.39120 1.464339 0.796731358  0.734408736
## 708   708      1 113.16186 13.03548 3.583279 0.350104789  1.618084239
## 709   709      1  60.89483 13.31298 3.457367 0.819466512 -0.934459593
## 710   710      1 102.88727 15.19005 7.894246 0.506226445 -3.142365978
## 711   711      1  90.44230 15.42025 3.606316 0.757747906 -1.063678666
## 712   712      1 100.15040 14.26107 5.592955 0.958778950 -2.024617171
## 713   713      1 100.45306 14.14267 7.887285 0.967471450 -1.160155698
## 714   714      1 115.42234 13.73483 5.694462 0.274761826 -2.277526094
## 715   715      1  99.68531 11.23610 5.120868 0.141498126  1.845598973
## 716   716      1  61.87310 15.49049 9.360025 0.880168887  2.687201553
## 717   717      1  92.21379 13.32397 3.456941 0.943498643 -1.791930129
## 718   718      1 113.08168 10.99205 2.796868 0.575637904 -2.719057013
## 719   719      1  93.80151 10.31319 3.970715 0.068930513  1.761884016
## 720   720      1 119.33399 11.59464 1.514538 0.860082512 -0.822072501
## 721   721      1 120.66363 15.46509 6.436386 0.247315433 -3.392295821
## 722   722      1  68.18178 15.83698 3.948586 0.946226032  1.804828586
## 723   723      1  86.42346 12.89580 8.006320 0.698543977  2.774106431
## 724   724      1 117.25587 10.68027 7.536443 0.786728258  0.236009351
## 725   725      1 113.12018 15.79698 4.447335 0.648623538 -0.824536988
## 726   726      1 118.84996 14.51341 3.870766 0.583774102 -1.925611042
## 727   727      1  97.41712 14.99895 6.181041 0.049262422 -2.933390453
## 728   728      1 126.59693 12.10229 6.685551 0.605355898 -2.014270044
## 729   729      1  92.56068 12.95225 3.316393 0.600832550  1.975496695
## 730   730      1 114.16979 13.95435 5.310274 0.669457132  0.245743356
## 731   731      1  74.23831 12.99144 1.209058 0.926584445  0.886005981
## 732   732      1  64.80089 11.26891 8.339061 0.083895234 -1.498962621
## 733   733      1  76.01434 14.08214 8.414146 0.527010944  1.349385714
## 734   734      1  64.60689 11.02725 5.049899 0.337871642 -2.671991386
## 735   735      1  69.80955 11.34497 2.834543 0.276031733 -2.815077174
## 736   736      1  95.82437 10.46171 5.364932 0.145861991  2.930365834
## 737   737      1  64.51909 13.54745 6.127444 0.631609143 -3.249308875
## 738   738      1  96.76814 11.44662 3.746455 0.288773036 -0.759417042
## 739   739      1 125.12454 13.73646 9.941703 0.678399548 -2.998015444
## 740   740      1 111.98382 10.93114 2.317100 0.461637762  0.022783148
## 741   741      1 110.43015 12.19728 2.277675 0.420070658  2.070793728
## 742   742      1  81.54323 14.78346 5.865412 0.858067909 -1.926970153
## 743   743      1  93.34460 15.32483 6.655722 0.216228077 -1.381423409
## 744   744      1 117.80161 15.49349 8.145523 0.745576130  1.313749812
## 745   745      1 118.43294 13.89803 1.399790 0.760412545 -0.714996649
## 746   746      1  76.26346 13.45661 2.279751 0.521217529  0.730690652
## 747   747      1  99.85276 15.16965 1.372274 0.599436574 -3.835138558
## 748   748      1 107.93320 10.59285 1.671725 0.784783754  0.691425541
## 749   749      1  77.29535 12.22027 7.205434 0.296947941 -1.647112498
## 750   750      1  83.80133 13.93298 5.434671 0.165262563  0.581366048
## 751   751      1  90.35914 15.45105 9.617765 0.739081182 -0.712120503
## 752   752      1  90.54078 12.89464 8.898616 0.339617966  0.653473519
## 753   753      1 127.18688 15.45633 1.810817 0.380740592  1.845939418
## 754   754      1 129.81736 13.97740 9.107462 0.533824399  0.301885324
## 755   755      1  62.28284 11.71465 5.784655 0.126382711  0.095108339
## 756   756      1 102.91196 12.34072 5.523952 0.689560780 -2.762573030
## 757   757      1 112.00049 13.87945 8.419225 0.870230646  0.926028441
## 758   758      1  65.63966 12.78283 3.451166 0.085905329  1.222927790
## 759   759      1  67.95763 10.86973 9.434878 0.018813415 -0.707746807
## 760   760      1  92.24004 15.56455 9.386492 0.383654911 -2.540284348
## 761   761      1  70.07838 10.75345 8.984368 0.979450461 -2.065785020
## 762   762      1  99.18538 15.87145 8.509946 0.265763845 -0.247612237
## 763   763      1  78.17739 11.60416 8.820454 0.261391284 -1.285820382
## 764   764      1 115.12666 12.30540 1.491357 0.147621043 -4.784117981
## 765   765      1 116.54013 14.28847 5.916094 0.879986943 -0.961035995
## 766   766      1 101.16522 13.16351 7.000342 0.757895573 -1.914839942
## 767   767      1 128.71937 10.81737 1.321057 0.007376764  3.481907165
## 768   768      1 118.72916 10.33225 4.628460 0.946930036 -0.999955675
## 769   769      1  79.04001 12.36624 5.190010 0.921786223 -0.844231863
## 770   770      1 119.75313 14.89535 3.722332 0.745224422  3.232587937
## 771   771      1  73.11096 10.43979 7.294592 0.927307247  1.562407100
## 772   772      1 121.52245 12.31770 8.904658 0.223819796 -1.861876999
## 773   773      1 116.42890 14.21476 3.856192 0.646500705  3.628689023
## 774   774      1  67.67417 14.51048 3.260990 0.955877439  2.151393541
## 775   775      1 123.90623 10.80742 6.728148 0.223675688  0.934398843
## 776   776      1 114.18753 15.58507 1.888599 0.530400806 -3.298535360
## 777   777      1  80.03984 14.31675 5.153271 0.374249028  0.353023278
## 778   778      1 100.82998 14.15958 7.227927 0.379095614 -2.752136463
## 779   779      1  89.89011 15.95738 1.007749 0.775276299  1.669273503
## 780   780      1 106.94156 11.75202 4.708048 0.178713327 -3.274778552
## 781   781      1  84.48934 10.22288 2.868033 0.214547804  0.764700496
## 782   782      1  72.41813 10.86631 7.919526 0.033449943  4.408555059
## 783   783      1  99.82228 15.58456 7.305010 0.074730873  4.284372083
## 784   784      1 113.43736 11.07421 5.784042 0.728657798 -2.079603634
## 785   785      1  64.69823 12.65759 2.467650 0.305028839 -1.421859500
## 786   786      1  75.46050 11.25597 7.973237 0.343189279  0.024790398
## 787   787      1 114.91221 13.21048 5.100130 0.528802793 -0.931324488
## 788   788      1 117.46461 15.22909 1.404643 0.821001653 -1.796003839
## 789   789      1  90.01676 10.03857 2.064083 0.380905771  0.431652400
## 790   790      1 126.28512 14.40055 8.244711 0.091260119 -0.981719332
## 791   791      1  84.92561 13.24895 9.545487 0.484181121  0.789956072
## 792   792      1  90.50529 13.29449 7.044221 0.888143817  1.156264785
## 793   793      1  74.94761 11.00718 6.996510 0.183917166  0.753865074
## 794   794      1  89.44987 10.11819 3.789966 0.900759106  0.969073834
## 795   795      1 117.51907 15.77435 4.575295 0.710756763 -1.166985842
## 796   796      1 119.35231 12.79235 5.653651 0.197735796  4.001080483
## 797   797      1 101.51062 13.67367 4.370296 0.307259406 -1.152217749
## 798   798      1  71.18890 15.97968 2.340614 0.934100420  0.636037469
## 799   799      1 117.20777 13.56837 4.345823 0.334281497  0.762162670
## 800   800      1 111.79070 14.35494 5.867418 0.094079197 -0.540540765
## 801   801      1  90.19829 13.47963 9.128835 0.199261877  0.854404420
## 802   802      1  63.76208 13.10670 1.566459 0.361100778 -0.341188404
## 803   803      1  87.87879 10.34009 1.751926 0.165347406 -0.704232592
## 804   804      1  92.74724 13.04732 1.489515 0.790722335 -0.292638369
## 805   805      1 125.37204 14.28691 1.883514 0.076147071 -2.415630757
## 806   806      1  95.70414 10.66772 8.836140 0.833280254  0.255755990
## 807   807      1  94.83547 10.99651 8.237204 0.903599565  0.206725805
## 808   808      1 111.26485 12.74728 9.515839 0.896159229  0.383055880
## 809   809      1 119.38825 14.34951 4.577364 0.099946887 -4.064852612
## 810   810      1  97.52845 12.98478 1.039920 0.765594074 -4.965654881
## 811   811      1  96.37634 11.18740 5.610330 0.613600101 -0.672887205
## 812   812      1 121.45111 14.59983 8.571083 0.034323357  0.142411124
## 813   813      1  74.01026 12.91856 5.463008 0.277183793  0.193103394
## 814   814      1  90.16813 14.86607 8.784449 0.266558505 -2.102536820
## 815   815      1  98.78566 12.87281 1.480893 0.304596241 -1.151559239
## 816   816      1 109.64603 15.39135 7.480122 0.603493642 -3.053381519
## 817   817      1  68.06376 15.75714 9.759064 0.120329102 -0.406477724
## 818   818      1  99.39315 10.22062 6.359835 0.034739005 -1.161136142
## 819   819      1 109.53204 13.36598 9.904824 0.808067198 -0.254125421
## 820   820      1  61.60051 12.40140 3.414683 0.704241985 -5.201512755
## 821   821      1 126.19986 10.55646 9.597852 0.149063971 -0.166835304
## 822   822      1 121.23712 14.32219 8.657806 0.382685058 -0.771510011
## 823   823      1  73.29254 15.69355 8.914273 0.115114406  1.134344264
## 824   824      1  93.04846 10.56928 7.638010 0.364100066 -3.505517076
## 825   825      1  68.40508 14.37989 9.323273 0.625478977  0.021003991
## 826   826      1 109.01540 13.96434 8.093268 0.802281764  1.749272367
## 827   827      1  91.74212 15.37827 1.678453 0.627345562 -1.347390423
## 828   828      1 128.45766 11.39661 6.191793 0.858417803 -4.574479374
## 829   829      1  81.03610 12.99268 2.170442 0.737306650  1.103839993
## 830   830      1  77.67747 14.60642 3.459082 0.084442680  0.146617812
## 831   831      1  82.53797 11.00755 4.496456 0.088625142  2.512056475
## 832   832      1 115.79180 14.43925 8.119670 0.333157307  0.344339410
## 833   833      1 101.27481 10.26034 2.641293 0.448123192  1.707180117
## 834   834      1  65.18917 10.60880 6.505170 0.144052125 -2.348311184
## 835   835      1  65.12984 11.99591 6.704008 0.767968429 -1.448789447
## 836   836      1  87.35301 10.42211 1.171016 0.258675485 -0.034677057
## 837   837      1  98.14375 14.52648 5.294619 0.632369466 -2.071737325
## 838   838      1  76.57848 10.32408 4.950282 0.511755201 -0.214540182
## 839   839      1  71.41934 11.37178 4.276880 0.731258655 -4.726200367
## 840   840      1  92.71166 11.40524 6.706767 0.624363769  4.348925192
## 841   841      1  89.16617 15.41894 2.473601 0.454263484  1.360967536
## 842   842      1  78.77430 10.68532 1.678620 0.751182706 -0.516422160
## 843   843      1  86.54380 12.90789 3.774293 0.204043892  1.070929665
## 844   844      1 112.22534 10.98999 6.261843 0.465179404 -0.544372591
## 845   845      1 114.24759 14.55753 9.855137 0.744593292 -3.309382084
## 846   846      1 107.24334 14.76041 3.406785 0.223212030 -0.029637332
## 847   847      1  67.47713 14.16465 5.287874 0.133215721 -0.400701112
## 848   848      1  79.20286 12.40423 8.253723 0.640957363 -1.472053541
## 849   849      1  91.48384 15.35620 1.430788 0.740589264  0.159789538
## 850   850      1 105.07031 12.39970 6.104247 0.217714895  0.748622401
## 851   851      1  96.99809 12.46681 6.705758 0.143792724 -3.184569640
## 852   852      1  74.55964 13.91507 2.702395 0.709151715 -3.081350464
## 853   853      1  94.36184 15.17391 2.468331 0.416583213 -0.896775984
## 854   854      1  93.95225 10.72583 1.501133 0.615675966  3.019130459
## 855   855      1  92.55526 13.75733 5.725047 0.208611771 -1.430971348
## 856   856      1 121.87679 12.28687 8.347025 0.910764635  1.127686464
## 857   857      1 119.16454 13.61097 2.264540 0.088515131  1.001427451
## 858   858      1  65.48211 15.39274 9.820744 0.104241883  0.237653100
## 859   859      1 123.13018 15.45984 3.483754 0.378566603 -0.421331238
## 860   860      1 112.94588 10.39896 8.492345 0.295793874 -1.729449820
## 861   861      1  99.79611 11.85426 2.751139 0.560907013 -0.934284470
## 862   862      1 128.81218 12.05116 1.294432 0.647632089  0.578774768
## 863   863      1 102.53941 15.63125 4.045210 0.585214156 -2.472602550
## 864   864      1  74.32467 11.12584 7.873902 0.293241639 -2.689835794
## 865   865      1  85.61050 12.72429 2.235214 0.262277252 -2.535616946
## 866   866      1  74.25184 15.77992 8.642372 0.676780788  1.470308347
## 867   867      1  61.16482 10.20879 4.207782 0.672808917  3.120922936
## 868   868      1 101.62661 14.16146 8.437116 0.605661437  1.423287251
## 869   869      1 117.92963 13.67679 5.082756 0.949521262  0.269971670
## 870   870      1 119.96284 15.21376 8.512934 0.463967651 -1.640499234
## 871   871      1 104.54214 13.79753 3.503403 0.781583922 -0.210387683
## 872   872      1 101.12190 13.71672 3.055512 0.680438018  2.316706730
## 873   873      1 121.67386 11.70690 6.745709 0.925691732  0.375086776
## 874   874      1  78.09958 15.94691 6.174866 0.125229423 -2.821487592
## 875   875      1 122.62052 14.91876 5.320221 0.541878721 -1.377619686
## 876   876      1  71.28362 15.09083 6.560714 0.423920387 -2.043265481
## 877   877      1  84.01508 11.21675 1.672829 0.622960636  1.461679562
## 878   878      1  83.83640 14.94265 7.599268 0.665447699  1.403103073
## 879   879      1  95.07062 13.86073 8.711093 0.526958557 -3.125422698
## 880   880      1  74.75525 12.98821 6.174287 0.878476901  1.147747714
## 881   881      1  77.21824 11.39968 3.280870 0.203675221  0.588050715
## 882   882      1  66.47000 13.47943 3.177382 0.404835815  2.175125199
## 883   883      1  92.19110 12.78977 2.949719 0.057408864 -1.675002772
## 884   884      1  96.65097 15.62883 5.286923 0.920611986  0.673858696
## 885   885      1  70.29789 11.22277 2.803686 0.395449435 -0.439927631
## 886   886      1  84.78877 15.17089 7.752864 0.654078089  3.915035618
## 887   887      1 120.07888 10.74301 5.257067 0.005722257 -1.067701561
## 888   888      1 118.58783 10.77244 5.289815 0.780552653  0.793250328
## 889   889      1  63.40451 14.21686 1.701985 0.431208034 -2.205932997
## 890   890      1  82.41529 12.63001 7.766875 0.992183518  1.511988130
## 891   891      1 104.29864 11.06799 9.910165 0.010758920 -1.296039206
## 892   892      1  69.72484 15.02634 9.403935 0.141744281 -0.257333347
## 893   893      1  71.53668 12.22239 9.294540 0.157567139 -3.693204494
## 894   894      1 107.24620 10.28885 7.401250 0.039415686 -4.700594881
## 895   895      1 120.34082 10.68642 2.544550 0.427128974 -2.060501769
## 896   896      1  73.53097 15.13595 7.237829 0.998152871 -4.288105663
## 897   897      1  65.41864 15.44727 1.719038 0.126029180  0.362953544
## 898   898      1 104.28854 13.29002 5.797906 0.287970854  5.756501934
## 899   899      1  90.21635 13.54459 6.015179 0.053334902 -1.694156487
## 900   900      1 100.83311 15.24228 5.449754 0.666488632 -2.223110110
## 901   901      1 114.41333 10.69565 1.732085 0.415926708 -2.266569900
## 902   902      1 111.46711 14.17553 9.513986 0.526330660  1.161932739
## 903   903      1  98.81215 13.18665 1.494027 0.076828237 -2.346372999
## 904   904      1  64.03158 12.29729 8.623670 0.102929856  1.589964820
## 905   905      1  86.99765 13.73239 1.757368 0.878986786  1.221692171
## 906   906      1 121.38694 13.83314 8.394354 0.383608091  1.568780165
## 907   907      1  91.27185 13.46409 8.763861 0.767016722  1.786692263
## 908   908      1 113.17632 11.88341 1.287098 0.218049144 -0.990599133
## 909   909      1  88.93991 10.84951 1.029684 0.642272612 -4.110581539
## 910   910      1 110.67754 12.81983 1.265764 0.268889623  0.086169798
## 911   911      1  70.11585 15.43343 2.216005 0.333870495  3.518023997
## 912   912      1 116.44888 13.08352 5.204555 0.250105321 -0.881242793
## 913   913      1 110.04359 10.07145 8.329173 0.120456074  1.251462293
## 914   914      1  80.96256 12.51769 9.326745 0.607120472 -3.869876781
## 915   915      1  63.21167 10.47517 6.008244 0.522385150 -2.209223085
## 916   916      1 122.56117 11.29591 7.780740 0.813681706 -1.849116334
## 917   917      1 129.87233 11.95807 6.005015 0.609153562 -1.430360145
## 918   918      1  93.75220 11.11547 1.074807 0.226861587 -0.193399202
## 919   919      1  70.88462 11.63757 6.023085 0.677396464  0.431072655
## 920   920      1  83.87471 11.93908 8.325315 0.185537605 -1.215507279
## 921   921      1 110.97024 11.13914 3.658291 0.110714613  1.409657751
## 922   922      1 129.71463 12.73283 9.727714 0.336949135 -0.580232927
## 923   923      1  83.03318 10.02726 6.955190 0.950538547  0.074888340
## 924   924      1 123.80664 10.42603 9.424200 0.105615841  0.457216781
## 925   925      1  77.89265 11.74614 6.069410 0.252598227  4.147622427
## 926   926      1 115.28366 15.39517 2.033917 0.257623724  0.045996273
## 927   927      1  76.38479 15.39390 5.012366 0.945176459 -2.127657940
## 928   928      1  80.55940 10.09145 2.013794 0.001914541  0.960030977
## 929   929      1 108.91811 11.64846 3.426814 0.317932076  0.340027280
## 930   930      1  98.50044 15.49657 4.267978 0.716065221  1.408303306
## 931   931      1  78.91219 15.55249 9.946626 0.868492966  0.424315288
## 932   932      1 120.66532 11.07238 8.878380 0.035590990  3.512141793
## 933   933      1  73.75692 13.56749 9.265682 0.440328413 -2.459159483
## 934   934      1  68.80176 11.76999 5.851564 0.056297863 -2.103246120
## 935   935      1 129.42510 15.30974 2.751297 0.292849531 -1.036463181
## 936   936      1  92.67379 15.65476 1.780371 0.461245523  0.283456529
## 937   937      1  95.67407 12.15663 3.617341 0.796629138  0.826859049
## 938   938      1  79.14280 12.77758 9.890854 0.485043163 -0.370212212
## 939   939      1  67.65379 12.12713 7.286760 0.832663578 -1.530505460
## 940   940      1  72.06208 11.33001 5.753785 0.511623349  4.272432473
## 941   941      1  74.53368 14.49385 2.143333 0.356089468  0.442784106
## 942   942      1  91.36585 11.69451 9.376978 0.687910163  3.933435294
## 943   943      1 120.21630 11.75846 3.002397 0.638017626  0.255269465
## 944   944      1  98.75673 11.02294 8.725410 0.372632533 -1.334693660
## 945   945      1  94.39775 10.35349 9.216918 0.301751507  3.383828247
## 946   946      1  80.05900 15.90847 5.332174 0.226386187 -0.325884975
## 947   947      1  72.50384 14.11759 2.582663 0.333709213  4.535242607
## 948   948      1  75.37519 13.71110 6.505098 0.663000267  3.123393576
## 949   949      1  65.13319 14.27275 6.727987 0.900412282  2.482000795
## 950   950      1  84.59058 15.91783 3.807610 0.518788734 -2.084669103
## 951   951      1  74.38828 14.43660 4.407224 0.877551880 -2.244348393
## 952   952      1  75.93456 14.64013 3.075730 0.671435782  0.006621030
## 953   953      1 127.28339 12.47715 4.169853 0.544177347  2.757989920
## 954   954      1 128.92154 11.68123 6.772124 0.216609929 -1.903952635
## 955   955      1  83.94540 13.70128 8.700648 0.595246030 -0.955095474
## 956   956      1 126.34935 11.03850 5.309696 0.978473313  3.338406516
## 957   957      1  70.63722 13.65395 6.627876 0.821529897 -3.860889441
## 958   958      1  88.97862 10.40602 4.147083 0.144622922 -0.350320106
## 959   959      1 104.49527 12.14331 9.782972 0.908846331  0.160956083
## 960   960      1  76.57934 11.75208 3.891431 0.112736960  3.155822815
## 961   961      1  72.11622 13.57673 3.898254 0.021588273 -1.499158511
## 962   962      1  74.26400 14.42352 7.471447 0.250686914  1.243451628
## 963   963      1  83.64364 14.47746 1.955308 0.763441024 -1.719764456
## 964   964      1 109.41718 14.00595 4.408295 0.687606095  0.493106816
## 965   965      1  65.12206 14.91102 9.111260 0.301607602  0.740774652
## 966   966      1  61.43753 15.49483 6.933485 0.374322119  2.811566835
## 967   967      1  93.03626 15.13573 3.043136 0.666912356 -0.594958824
## 968   968      1 123.13960 10.87152 1.697125 0.007377125  2.643058468
## 969   969      1  70.98749 12.88016 6.749655 0.572886677 -1.947866004
## 970   970      1 106.82765 13.60476 6.862334 0.593117550 -1.213043871
## 971   971      1 118.50941 15.58879 5.620605 0.741224982 -1.950799148
## 972   972      1  76.34706 10.10801 5.909858 0.703599191  0.272607959
## 973   973      1  86.41824 12.59145 2.825040 0.579643369 -0.945040998
## 974   974      1 118.41939 10.96633 7.405993 0.451689861 -0.939625230
## 975   975      1  97.90634 11.10660 7.834082 0.450998180  0.265335413
## 976   976      1 101.44528 12.54459 3.196640 0.184395137 -0.688734463
## 977   977      1  72.42409 10.18375 7.208135 0.778163290  0.268289023
## 978   978      1  70.34485 14.40771 8.585012 0.707927299  2.363364451
## 979   979      1 126.42486 15.05019 4.644646 0.690364105  3.019951129
## 980   980      1 121.98236 14.91701 5.406012 0.564030894  2.530836654
## 981   981      1  93.09335 12.45262 1.344221 0.493018524 -1.010269966
## 982   982      1 128.94232 14.17554 8.386386 0.213137395 -3.414064224
## 983   983      1  80.97413 12.88060 7.835285 0.033179208 -3.849693612
## 984   984      1 118.93061 10.11376 9.155902 0.668221077 -0.210345229
## 985   985      1  78.57775 14.09597 5.523923 0.581529382 -0.481916400
## 986   986      1 122.92140 15.52507 1.253460 0.746372288  2.728708307
## 987   987      1 103.83655 15.98425 9.567533 0.054324780  2.282255348
## 988   988      1  74.49775 14.63128 3.766158 0.937235031 -1.805180386
## 989   989      1  75.35345 12.92822 5.102801 0.462610280 -1.686451555
## 990   990      1  68.95041 15.26364 3.309202 0.575918101 -0.807806900
## 991   991      1  91.28304 14.12231 7.051300 0.047195424 -0.023588131
## 992   992      1 122.58400 12.20098 3.082280 0.501901606 -0.361099214
## 993   993      1  84.57114 10.44158 3.234570 0.428048074  2.558755152
## 994   994      1 116.11665 10.11563 9.269568 0.609655731  2.654057727
## 995   995      1 100.96747 14.98359 4.279481 0.040618361  1.003594978
## 996   996      1  99.64842 13.67727 3.460130 0.336970939  1.964597626
## 997   997      1 108.84549 15.89380 3.528101 0.205145500 -1.243980440
## 998   998      1 113.83624 10.85625 3.278173 0.489040898 -4.233866404
## 999   999      1  84.68313 13.84138 6.121114 0.541816804  2.008483621
## 1000 1000      1  71.49173 14.65108 4.611031 0.005188448  1.557143703
##      size_centered natural_mortality fishing_mortality total_mortality
## 1    -36.626896493          50.75459         13.662690        64.41728
## 2    -28.586241491          60.75847         12.858624        73.61710
## 3    -18.376486329          50.55845         11.837649        62.39610
## 4    -30.032233114          59.62270         13.003223        72.62592
## 5    -31.511039683          50.18073         13.151104        63.33183
## 6    -15.834645848          46.07224         11.583465        57.65570
## 7      4.160295613          42.00180          9.583970        51.58577
## 8     -5.302848564          45.94503         10.530285        56.47531
## 9    -28.198957194          60.70568         12.819896        73.52558
## 10   -50.097811827          62.59332         15.009781        77.60310
## 11   -44.270822275          54.34212         14.427082        68.76920
## 12     4.171195177          38.69422          9.582880        48.27710
## 13   -53.600839505          69.90934         15.360084        85.26943
## 14   -17.865280048          55.70882         11.786528        67.49535
## 15   -42.849636837          73.46856         14.284964        87.75352
## 16    -0.290409385          37.45765         10.029041        47.48670
## 17   -22.550329473          47.35370         12.255033        59.60874
## 18   -57.050578343          66.42813         15.705058        82.13318
## 19   -48.911496382          65.05044         14.891150        79.94159
## 20   -26.310932497          55.89607         12.631093        68.52717
## 21   -20.720991592          58.52593         12.072099        70.59803
## 22     7.202330534          28.67542          9.279767        37.95519
## 23     5.820500129          40.05339          9.417950        49.47134
## 24   -32.071571127          50.45516         13.207157        63.66232
## 25    -4.142926564          45.46294         10.414293        55.87723
## 26   -49.265003311          73.23709         14.926500        88.16359
## 27     5.628633166          34.10255          9.437137        43.53968
## 28    -3.675568600          45.22087         10.367557        55.58842
## 29   -31.282969438          58.64823         13.128297        71.77653
## 30   -50.317446918          73.14354         15.031745        88.17528
## 31   -25.933498228          50.01844         12.593350        62.61179
## 32    -9.190229089          59.88167         10.919023        70.80070
## 33    -8.864135200          48.26313         10.886414        59.14955
## 34   -57.625599522          67.25252         15.762560        83.01508
## 35   -55.944394227          73.88905         15.594439        89.48349
## 36     0.773562535          40.42230          9.922644        50.34494
## 37   -42.906300647          67.88167         14.290630        82.17230
## 38   -40.769654706          57.85871         14.076965        71.93568
## 39    -6.881958367          53.75864         10.688196        64.44683
## 40   -44.163070626          54.60261         14.416307        69.01892
## 41   -56.128892114          67.60778         15.612889        83.22067
## 42   -57.510638991          67.79178         15.751064        83.54284
## 43   -26.803173947          59.37855         12.680317        72.05887
## 44   -23.405238208          48.02321         12.340524        60.36374
## 45   -53.937071133          74.11798         15.393707        89.51168
## 46    -5.803822691          50.07804         10.580382        60.65842
## 47    -3.479879689          50.95842         10.347988        61.30641
## 48   -33.715068675          65.30895         13.371507        78.68046
## 49     4.234898710          40.39441          9.576510        49.97092
## 50    -2.769654510          52.02318         10.276965        62.30014
## 51   -33.626909808          72.31641         13.362691        85.67910
## 52   -58.077953332          73.02543         15.807795        88.83323
## 53     1.178612218          37.79411          9.882139        47.67625
## 54   -46.740837027          60.32018         14.674084        74.99427
## 55   -18.881204091          58.80127         11.888120        70.68939
## 56   -44.522034435          59.48655         14.452203        73.93876
## 57   -56.079698021          65.82917         15.607970        81.43714
## 58     5.374669945          53.99070          9.462533        63.45323
## 59   -22.073354023          63.42081         12.207335        75.62814
## 60   -57.126126080          62.66279         15.712613        78.37540
## 61   -38.022329053          56.36543         13.802233        70.16766
## 62    -5.002740340          40.29287         10.500274        50.79315
## 63   -23.802245930          53.42339         12.380225        65.80361
## 64    -9.635938064          55.81522         10.963594        66.77882
## 65   -27.885341523          65.14315         12.788534        77.93169
## 66    -0.929166758          53.57906         10.092917        63.67198
## 67   -57.972989383          78.51940         15.797299        94.31670
## 68   -42.786492771          58.04221         14.278649        72.32085
## 69   -20.566339325          46.64701         12.056634        58.70365
## 70   -51.382547468          65.08708         15.138255        80.22534
## 71     1.883145531          37.79507          9.811685        47.60675
## 72     3.158255096          48.65668          9.684174        58.34085
## 73   -43.819728149          62.84178         14.381973        77.22375
## 74   -57.739673108          66.77852         15.773967        82.55249
## 75   -42.265368220          71.40747         14.226537        85.63400
## 76   -33.302258451          63.40782         13.330226        76.73805
## 77     7.836353395          48.16154          9.216365        57.37791
## 78    -3.728857015          40.28376         10.372886        50.65664
## 79   -49.053004016          60.29918         14.905300        75.20448
## 80   -42.392598598          69.74461         14.239260        83.98387
## 81   -10.134639544          47.53596         11.013464        58.54943
## 82   -55.677508956          65.45758         15.567751        81.02533
## 83   -12.052636596          45.81992         11.205264        57.02518
## 84     7.117806333          43.51441          9.288219        52.80263
## 85   -59.866020316          72.84722         15.986602        88.83383
## 86   -33.358678115          51.66830         13.335868        65.00416
## 87   -31.029787012          64.16938         13.102979        77.27236
## 88    -6.756117195          50.03610         10.675612        60.71171
## 89   -32.065432349          57.36233         13.206543        70.56887
## 90   -41.331401519          66.90710         14.133140        81.04024
## 91   -40.387650307          63.10400         14.038765        77.14276
## 92   -54.621078041          66.30497         15.462108        81.76707
## 93   -45.344444832          65.52396         14.534444        80.05841
## 94    -9.117429936          53.60394         10.911743        64.51568
## 95   -26.302411892          53.68302         12.630241        66.31326
## 96   -52.111637963          75.91418         15.211164        91.12535
## 97    -4.014732428          56.14846         10.401473        66.54994
## 98   -52.958207882          63.66390         15.295821        78.95973
## 99     5.201359072          41.69666          9.479864        51.17652
## 100    3.260230504          38.09196          9.673977        47.76594
## 101  -27.940274454          50.74178         12.794027        63.53580
## 102  -53.460581466          57.04467         15.346058        72.39073
## 103  -44.846921919          61.76818         14.484692        76.25287
## 104  -25.160359372          55.02569         12.516036        67.54173
## 105  -23.303843569          49.70320         12.330384        62.03359
## 106  -30.775143751          64.90735         13.077514        77.98487
## 107  -29.239013689          55.92499         12.923901        68.84890
## 108  -26.244630078          54.32558         12.624463        66.95004
## 109   -6.901516484          55.72724         10.690152        66.41740
## 110  -16.168145011          44.95990         11.616815        56.57672
## 111  -44.058360700          69.36172         14.405836        83.76756
## 112  -31.088710120          46.61915         13.108871        59.72802
## 113    0.663830661          39.63334          9.933617        49.56695
## 114  -15.739474851          50.80532         11.573947        62.37927
## 115    7.246398763          45.47063          9.275360        54.74599
## 116  -37.692286482          52.62762         13.769229        66.39685
## 117  -23.749046666          48.48502         12.374905        60.85992
## 118   -5.311174130          47.06875         10.531117        57.59987
## 119   -0.762804013          49.37955         10.076280        59.45583
## 120  -38.183728002          68.81182         13.818373        82.63019
## 121  -22.635128265          61.19334         12.263513        73.45686
## 122    1.867909732          36.00581          9.813209        45.81901
## 123  -43.231676521          58.39267         14.323168        72.71584
## 124  -11.043419337          53.03937         11.104342        64.14372
## 125   -9.968681482          47.13580         10.996868        58.13267
## 126  -56.045487823          60.95557         15.604549        76.56012
## 127  -41.158533141          55.28156         14.115853        69.39741
## 128  -14.247875086          57.04377         11.424788        68.46856
## 129  -23.168554411          47.48992         12.316855        59.80678
## 130  -45.594771106          70.07432         14.559477        84.63379
## 131  -18.331725788          44.45276         11.833173        56.28593
## 132  -53.047628193          76.37439         15.304763        91.67916
## 133    9.072353279          40.11668          9.092765        49.20945
## 134  -25.452549648          53.55449         12.545255        66.09974
## 135   -0.487135737          50.60877         10.048714        60.65749
## 136  -41.832333710          63.03368         14.183233        77.21692
## 137  -41.209815613          55.92855         14.120982        70.04954
## 138    1.684042339          36.97536          9.831596        46.80696
## 139  -39.286302910          51.18171         13.928630        65.11034
## 140  -25.764434864          65.79512         12.576443        78.37156
## 141    3.505800620          30.20604          9.649420        39.85546
## 142  -33.601015608          63.29953         13.360102        76.65963
## 143  -25.083868999          66.76208         12.508387        79.27047
## 144  -20.905264320          48.32063         12.090526        60.41116
## 145  -29.317860855          48.82381         12.931786        61.75560
## 146  -50.417686524          68.05811         15.041769        83.09988
## 147  -12.655989688          57.25338         11.265599        68.51898
## 148   -5.204029977          51.85307         10.520403        62.37347
## 149   -0.913019860          48.36969         10.091302        58.46099
## 150  -16.042578756          53.07349         11.604258        64.67775
## 151  -28.990977239          63.50068         12.899098        76.39977
## 152  -28.126417280          48.56556         12.812642        61.37820
## 153  -46.146107544          68.17508         14.614611        82.78969
## 154  -52.546830885          64.59279         15.254683        79.84747
## 155  -25.996767220          64.56219         12.599677        77.16186
## 156  -39.526925986          51.76063         13.952693        65.71332
## 157  -41.118535406          55.35085         14.111854        69.46271
## 158    6.332003183          42.46161          9.366800        51.82841
## 159  -41.524419799          61.24892         14.152442        75.40136
## 160  -16.618645624          55.02682         11.661865        66.68868
## 161    5.044525901          36.65711          9.495547        46.15266
## 162  -38.540714390          50.91693         13.854071        64.77100
## 163    5.022362852          42.38112          9.497764        51.87888
## 164  -20.010275235          56.06112         12.001028        68.06215
## 165   -9.234394617          55.21160         10.923439        66.13504
## 166   -8.816489414          51.75274         10.881649        62.63439
## 167  -22.126479896          53.69159         12.212648        65.90424
## 168    5.874473294          38.75931          9.412553        48.17187
## 169  -41.173047796          66.61496         14.117305        80.73226
## 170  -19.562070591          53.90493         11.956207        65.86114
## 171   -2.028519735          43.08987         10.202852        53.29272
## 172  -50.288918286          51.57393         15.028892        66.60283
## 173   -3.035070633          39.60870         10.303507        49.91221
## 174    9.808755952          46.89415          9.019124        55.91327
## 175  -26.597200548          42.10484         12.659720        54.76456
## 176    2.781800102          37.77272          9.721820        47.49454
## 177  -14.448128666          42.75559         11.444813        54.20040
## 178  -32.598333890          53.89729         13.259833        67.15713
## 179  -51.099077384          59.67623         15.109908        74.78614
## 180  -19.693609334          50.91227         11.969361        62.88163
## 181  -11.623435165          44.05454         11.162344        55.21688
## 182   -2.481289571          38.93486         10.248129        49.18298
## 183  -49.777224283          70.66577         14.977722        85.64349
## 184    0.700712353          43.53605          9.929929        53.46597
## 185  -16.707653576          48.31511         11.670765        59.98588
## 186  -42.197407889          59.09123         14.219741        73.31097
## 187    1.318795416          51.58293          9.868120        61.45105
## 188  -48.540900375          63.33023         14.854090        78.18432
## 189  -58.293781828          68.38193         15.829378        84.21131
## 190  -13.077653847          43.29173         11.307765        54.59950
## 191    6.131035320          38.86469          9.386896        48.25159
## 192    4.214556115          37.49232          9.578544        47.07087
## 193  -50.407377458          62.07110         15.040738        77.11183
## 194  -33.266707812          57.03311         13.326671        70.35978
## 195   -6.337861158          44.91102         10.633786        55.54481
## 196    8.445668137          47.69660          9.155433        56.85203
## 197  -54.180934655          59.80953         15.418093        75.22762
## 198    6.086524352          40.28172          9.391348        49.67307
## 199  -38.769268608          55.13436         13.876927        69.01129
## 200  -10.893898834          39.82664         11.089390        50.91603
## 201  -29.681374927          63.95998         12.968137        76.92812
## 202    6.962258939          42.25762          9.303774        51.56140
## 203  -10.064190372          45.68542         11.006419        56.69184
## 204  -54.271044605          62.44615         15.427104        77.87325
## 205  -23.386361843          57.35997         12.338636        69.69861
## 206   -1.135935572          47.51386         10.113594        57.62745
## 207  -39.716301565          59.11135         13.971630        73.08298
## 208  -46.105115265          63.52815         14.610512        78.13866
## 209    0.295402308          37.26893          9.970460        47.23939
## 210   -6.178405420          47.13828         10.617841        57.75612
## 211  -48.432995360          67.37734         14.843300        82.22064
## 212  -43.356303254          64.84932         14.335630        79.18496
## 213  -21.321185045          47.48111         12.132119        59.61323
## 214  -12.984560065          57.30347         11.298456        68.60193
## 215  -23.102285159          46.53075         12.310229        58.84098
## 216   -4.531441811          41.42263         10.453144        51.87577
## 217  -47.573842735          70.97494         14.757384        85.73232
## 218  -44.495141110          56.53874         14.449514        70.98826
## 219  -40.032557666          63.84527         14.003256        77.84853
## 220    8.106381958          50.53325          9.189362        59.72261
## 221  -29.998367035          51.85213         12.999837        64.85197
## 222  -41.426620807          60.79104         14.142662        74.93370
## 223    7.907571383          53.70179          9.209243        62.91103
## 224   -3.433155206          38.22100         10.343316        48.56432
## 225  -42.555707076          61.59264         14.255571        75.84821
## 226  -13.206441724          51.75977         11.320644        63.08041
## 227  -56.492459644          66.62741         15.649246        82.27665
## 228  -31.263756696          58.75445         13.126376        71.88082
## 229  -45.146762349          60.60471         14.514676        75.11939
## 230  -26.568965674          63.67424         12.656897        76.33113
## 231    5.917004542          51.62362          9.408300        61.03192
## 232  -10.423990244          53.61805         11.042399        64.66045
## 233  -32.699581161          56.54077         13.269958        69.81073
## 234  -46.928052793          69.63336         14.692805        84.32617
## 235   -3.451578221          41.04753         10.345158        51.39269
## 236  -47.211900554          68.74173         14.721190        83.46292
## 237   -3.096183739          51.54007         10.309618        61.84968
## 238  -15.107952598          50.39392         11.510795        61.90471
## 239  -48.442356575          64.86463         14.844236        79.70887
## 240  -28.806762418          57.17097         12.880676        70.05165
## 241    7.036319373          30.11236          9.296368        39.40873
## 242    3.526547279          38.74206          9.647345        48.38940
## 243  -51.617567877          63.18128         15.161757        78.34304
## 244   -4.764400488          50.52622         10.476440        61.00266
## 245  -17.759266009          46.34639         11.775927        58.12231
## 246  -43.313393123          54.13169         14.331339        68.46303
## 247  -34.814933788          49.72086         13.481493        63.20236
## 248    9.527274829          36.43928          9.047273        45.48655
## 249  -23.934090394          47.65723         12.393409        60.05064
## 250  -43.440677642          60.50870         14.344068        74.85277
## 251  -14.242316864          55.07151         11.424232        66.49574
## 252  -32.359217382          59.86290         13.235922        73.09882
## 253  -23.424558796          57.25903         12.342456        69.60148
## 254  -17.397882154          52.69924         11.739788        64.43903
## 255  -17.851216949          60.53308         11.785122        72.31820
## 256  -27.530454679          57.92405         12.753045        70.67710
## 257  -24.552257343          49.72662         12.455226        62.18184
## 258  -55.870799415          58.87327         15.587080        74.46035
## 259  -33.525364508          47.04175         13.352536        60.39428
## 260    5.213849726          41.08247          9.478615        50.56109
## 261   -3.709878363          55.64328         10.370988        66.01427
## 262  -32.263010100          57.39502         13.226301        70.62132
## 263    1.811610789          32.70351          9.818839        42.52235
## 264   -3.490751497          57.28628         10.349075        67.63536
## 265  -18.070659868          47.36088         11.807066        59.16794
## 266  -42.394746270          71.40287         14.239475        85.64234
## 267  -59.531842531          69.64278         15.953184        85.59596
## 268  -18.402026207          58.18295         11.840203        70.02315
## 269  -18.742743200          55.95553         11.874274        67.82981
## 270   -2.791602651          50.35625         10.279160        60.63541
## 271    6.457566146          37.14893          9.354243        46.50317
## 272  -14.388143995          49.73912         11.438814        61.17793
## 273  -32.200382783          54.06951         13.220038        67.28955
## 274  -32.983011331          57.60862         13.298301        70.90692
## 275  -36.159462531          55.72925         13.615946        69.34520
## 276  -34.490888608          52.97031         13.449089        66.41940
## 277   -2.213605789          47.35003         10.221361        57.57139
## 278  -58.344018350          67.36584         15.834402        83.20024
## 279  -15.952689955          45.36394         11.595269        56.95921
## 280  -13.083358426          46.88040         11.308336        58.18873
## 281  -12.464380139          44.70551         11.246438        55.95195
## 282  -20.410606784          57.18179         12.041061        69.22285
## 283  -45.511540961          59.90322         14.551154        74.45438
## 284  -20.490946486          51.95918         12.049095        64.00827
## 285  -55.217178883          63.09747         15.521718        78.61918
## 286  -17.983090146          55.92244         11.798309        67.72075
## 287    9.115256206          38.31145          9.088474        47.39992
## 288  -14.051484100          50.72598         11.405148        62.13113
## 289   -9.721338926          46.28850         10.972134        57.26063
## 290  -41.430129814          60.46030         14.143013        74.60331
## 291    4.928469385          47.53613          9.507153        57.04328
## 292    3.136365970          42.39832          9.686363        52.08469
## 293  -28.510284328          63.34132         12.851028        76.19234
## 294    4.939942318          41.17258          9.506006        50.67859
## 295    6.070150894          38.01512          9.392985        47.40811
## 296  -29.450664138          63.40806         12.945066        76.35313
## 297    9.592006139          41.70227          9.040799        50.74307
## 298  -34.024448360          57.16959         13.402445        70.57203
## 299  -36.925558110          66.39488         13.692556        80.08744
## 300  -31.684414721          61.41644         13.168441        74.58488
## 301  -38.597633706          49.57916         13.859763        63.43892
## 302  -15.905242567          46.73410         11.590524        58.32462
## 303  -23.025800751          50.89726         12.302580        63.19984
## 304    6.425043051          43.01311          9.357496        52.37061
## 305  -51.649146478          55.97738         15.164915        71.14230
## 306  -22.827850212          49.00483         12.282785        61.28761
## 307  -33.769588235          63.98390         13.376959        77.36086
## 308    2.902728687          37.45838          9.709727        47.16811
## 309  -54.869070568          63.84373         15.486907        79.33064
## 310    4.167479770          34.70246          9.583252        44.28571
## 311  -59.898653473          60.84636         15.989865        76.83622
## 312    9.803011753          45.23358          9.019699        54.25328
## 313  -34.806689371          63.13485         13.480669        76.61552
## 314  -12.101461960          49.47482         11.210146        60.68496
## 315  -22.884664617          48.48542         12.288466        60.77388
## 316  -44.408074366          64.15599         14.440807        78.59680
## 317  -55.424365303          67.01546         15.542437        82.55790
## 318  -49.009616871          71.28808         14.900962        86.18904
## 319  -39.700144546          58.50716         13.970014        72.47717
## 320    7.886060863          36.99113          9.211394        46.20252
## 321  -17.189896358          56.12425         11.718990        67.84324
## 322  -22.903641020          54.01092         12.290364        66.30128
## 323   -2.504319192          38.84577         10.250432        49.09620
## 324  -32.485832048          61.21515         13.248583        74.46374
## 325  -20.871046446          60.90978         12.087105        72.99689
## 326  -30.241082467          47.05465         13.024108        60.07876
## 327  -11.144741091          49.02879         11.114474        60.14326
## 328   -8.966564902          45.45616         10.896656        56.35282
## 329  -29.663641485          69.32111         12.966364        82.28748
## 330  -47.385715349          69.64025         14.738572        84.37882
## 331  -28.459382011          47.77688         12.845938        60.62281
## 332  -38.709822737          54.75495         13.870982        68.62593
## 333   -9.010990956          38.66511         10.901099        49.56621
## 334  -23.947149315          47.47652         12.394715        59.87123
## 335  -12.089770599          41.53159         11.208977        52.74057
## 336  -58.859772531          69.16315         15.885977        85.04913
## 337  -10.787438927          58.37365         11.078744        69.45240
## 338   -7.147381108          50.81369         10.714738        61.52843
## 339   -5.192275527          44.15353         10.519228        54.67276
## 340   -3.420229000          44.60006         10.342023        54.94208
## 341  -21.780916161          51.21529         12.178092        63.39338
## 342  -13.834533151          41.58913         11.383453        52.97258
## 343  -49.478417237          56.71686         14.947842        71.66470
## 344  -28.894327870          54.86698         12.889433        67.75641
## 345  -25.889904732          44.87384         12.588990        57.46283
## 346    6.282009943          36.94112          9.371799        46.31292
## 347   -3.084951025          39.17988         10.308495        49.48838
## 348  -24.681304148          55.80892         12.468130        68.27705
## 349  -58.976835262          71.47616         15.897684        87.37385
## 350  -29.091599965          56.85424         12.909160        69.76340
## 351   -8.260312721          48.89319         10.826031        59.71922
## 352  -38.976597115          61.12170         13.897660        75.01936
## 353   -7.696568505          44.10121         10.769657        54.87086
## 354   -7.641281970          54.26572         10.764128        65.02985
## 355  -54.207226562          67.29298         15.420723        82.71371
## 356  -41.679501669          60.20309         14.167950        74.37104
## 357  -57.191187134          69.80242         15.719119        85.52154
## 358  -51.317689065          61.87493         15.131769        77.00670
## 359   -8.122839448          52.71281         10.812284        63.52509
## 360  -24.223481137          50.09774         12.422348        62.52009
## 361  -45.605686919          70.76070         14.560569        85.32127
## 362  -45.636544051          62.66832         14.563654        77.23197
## 363  -44.496998822          67.35224         14.449700        81.80194
## 364  -29.266065676          58.28407         12.926607        71.21068
## 365  -35.405914811          66.87298         13.540591        80.41357
## 366  -47.379168351          56.24424         14.737917        70.98216
## 367  -42.088748971          50.91294         14.208875        65.12181
## 368  -39.007887859          57.22225         13.900789        71.12304
## 369   -5.695623169          41.24674         10.569562        51.81631
## 370   -2.246019214          53.71066         10.224602        63.93526
## 371    4.844435579          41.18840          9.515556        50.70396
## 372   -9.631623439          45.00392         10.963162        55.96708
## 373  -14.469148873          48.96345         11.446915        60.41036
## 374  -42.823863472          69.83587         14.282386        84.11826
## 375    9.761752167          36.31450          9.023825        45.33833
## 376   -3.550708592          42.66713         10.355071        53.02220
## 377  -31.062557269          52.12899         13.106256        65.23525
## 378  -34.335148130          56.60594         13.433515        70.03945
## 379  -31.708688608          55.09202         13.170869        68.26289
## 380  -55.064265872          73.32897         15.506427        88.83539
## 381   -9.972947212          52.81349         10.997295        63.81079
## 382  -14.193754015          53.57931         11.419375        64.99868
## 383  -27.763650087          60.07697         12.776365        72.85333
## 384   -8.386745614          42.45471         10.838675        53.29339
## 385  -33.456453881          60.75489         13.345645        74.10053
## 386  -24.331553762          59.29155         12.433155        71.72470
## 387    5.434490102          36.22150          9.456551        45.67805
## 388  -12.025015070          53.42205         11.202502        64.62455
## 389  -53.415607337          64.27115         15.341561        79.61271
## 390  -40.656512608          61.85237         14.065651        75.91802
## 391  -10.060862796          48.44604         11.006086        59.45213
## 392  -20.650452031          53.78202         12.065045        65.84707
## 393  -29.289459300          66.89978         12.928946        79.82873
## 394  -38.978508040          68.76396         13.897851        82.66181
## 395  -44.275406047          53.06371         14.427541        67.49125
## 396    9.010911798          39.46773          9.098909        48.56664
## 397  -49.478714825          59.72296         14.947871        74.67083
## 398  -53.895711689          67.95949         15.389571        83.34906
## 399   -3.804134952          50.37550         10.380413        60.75592
## 400  -39.851972507          50.34103         13.985197        64.32623
## 401  -21.351195700          61.63583         12.135120        73.77095
## 402    4.188844813          49.99208          9.581116        59.57320
## 403    7.281468590          34.99974          9.271853        44.27160
## 404    3.641803018          36.46846          9.635820        46.10428
## 405  -41.523076359          69.40379         14.152308        83.55610
## 406  -19.104987646          48.38636         11.910499        60.29686
## 407  -49.697387281          62.85975         14.969739        77.82949
## 408  -56.860968608          64.67100         15.686097        80.35710
## 409  -18.353164303          62.53798         11.835316        74.37329
## 410  -16.440689520          59.77716         11.644069        71.42123
## 411  -37.457691862          59.69600         13.745769        73.44177
## 412  -15.258183228          52.30004         11.525818        63.82586
## 413  -29.583784519          48.11582         12.958378        61.07419
## 414  -17.186738593          47.48379         11.718674        59.20246
## 415  -43.529610427          65.81727         14.352961        80.17024
## 416  -30.615596874          45.71511         13.061560        58.77667
## 417  -23.978634838          46.43423         12.397863        58.83209
## 418  -49.076996874          64.10997         14.907700        79.01767
## 419  -40.892625530          69.44875         14.089263        83.53801
## 420   -8.104352430          44.60225         10.810435        55.41268
## 421   -7.043816794          53.79040         10.704382        64.49479
## 422    0.045908575          43.94905          9.995409        53.94446
## 423   -6.719212083          44.73399         10.671921        55.40591
## 424    9.964022497          34.76395          9.003598        43.76755
## 425  -26.614043654          53.25960         12.661404        65.92100
## 426  -54.710668277          63.50399         15.471067        78.97505
## 427  -29.272292056          54.90895         12.927229        67.83618
## 428  -35.358073204          59.97764         13.535807        73.51345
## 429   -9.283078448          48.94951         10.928308        59.87782
## 430   -5.276667844          41.39719         10.527667        51.92486
## 431    9.136572697          33.33424          9.086343        42.42059
## 432    9.511895687          36.25276          9.048810        45.30157
## 433    8.918627708          36.03061          9.108137        45.13875
## 434  -25.555579823          49.14464         12.555558        61.70020
## 435  -11.990882044          39.59333         11.199088        50.79242
## 436  -44.767768495          62.01591         14.476777        76.49268
## 437  -30.641572450          55.44962         13.064157        68.51378
## 438    5.242961147          43.96374          9.475704        53.43945
## 439  -42.281738762          59.99467         14.228174        74.22284
## 440    7.221752431          43.34000          9.277825        52.61782
## 441   -1.994527932          43.15643         10.199453        53.35589
## 442  -48.308667617          57.26825         14.830867        72.09912
## 443  -47.901435206          65.56820         14.790144        80.35834
## 444  -52.710543633          68.26062         15.271054        83.53168
## 445  -18.439677774          54.75048         11.843968        66.59445
## 446  -39.432431883          51.87522         13.943243        65.81847
## 447  -34.251995825          62.30359         13.425200        75.72879
## 448  -51.439882126          62.70610         15.143988        77.85009
## 449  -24.920798871          48.92553         12.492080        61.41761
## 450    5.344433903          45.56781          9.465557        55.03336
## 451  -14.065775552          48.65679         11.406578        60.06337
## 452  -22.877748075          56.04538         12.287775        68.33315
## 453  -59.926613967          67.19271         15.992661        83.18537
## 454  -28.904431676          59.37579         12.890443        72.26623
## 455  -17.083053412          58.23440         11.708305        69.94271
## 456    8.313109537          44.68993          9.168689        53.85862
## 457  -17.376654781          52.37321         11.737665        64.11088
## 458    2.426583220          37.70283          9.757342        47.46017
## 459  -28.724874686          62.15391         12.872487        75.02640
## 460  -41.069041721          65.14592         14.106904        79.25283
## 461   -9.468095056          60.00517         10.946810        70.95198
## 462  -13.401323843          58.60716         11.340132        69.94729
## 463    3.508759239          43.25991          9.649124        52.90903
## 464  -20.878820776          46.41142         12.087882        58.49930
## 465   -5.238646814          42.91005         10.523865        53.43392
## 466  -45.135711131          65.13504         14.513571        79.64861
## 467  -57.727113822          72.90730         15.772711        88.68002
## 468  -12.643546071          44.22514         11.264355        55.48950
## 469  -45.606887636          65.28808         14.560689        79.84877
## 470  -15.564686339          48.74403         11.556469        60.30050
## 471  -21.904625830          51.03860         12.190463        63.22906
## 472  -57.986274816          72.85884         15.798627        88.65747
## 473    7.012774111          47.26274          9.298723        56.56147
## 474  -59.371057076          66.81118         15.937106        82.74829
## 475  -39.788147195          71.26523         13.978815        85.24404
## 476  -22.904225341          51.21872         12.290423        63.50914
## 477  -36.622179353          61.75342         13.662218        75.41564
## 478  -15.238588441          53.55131         11.523859        65.07517
## 479  -31.519028740          60.89256         13.151903        74.04446
## 480  -48.281498544          71.91754         14.828150        86.74569
## 481  -25.235540287          43.27763         12.523554        55.80118
## 482    8.856320470          40.03939          9.114368        49.15376
## 483  -57.547282029          70.67942         15.754728        86.43414
## 484  -28.459048665          63.56447         12.845905        76.41037
## 485    2.021494748          37.17654          9.797851        46.97439
## 486    3.992364595          41.43097          9.600764        51.03174
## 487  -37.994396689          55.24059         13.799440        69.04003
## 488  -22.462782455          43.95557         12.246278        56.20185
## 489  -56.322586392          68.46828         15.632259        84.10054
## 490  -48.968346757          61.05924         14.896835        75.95607
## 491  -45.116393315          63.07535         14.511639        77.58699
## 492  -23.252000848          52.11236         12.325200        64.43756
## 493    4.066242115          43.22619          9.593376        52.81956
## 494    8.862187199          36.70678          9.113781        45.82056
## 495  -18.327689895          58.60564         11.832769        70.43841
## 496    5.476116950          42.15144          9.452388        51.60383
## 497  -53.987731016          56.01417         15.398773        71.41294
## 498  -43.389233542          69.03450         14.338923        83.37342
## 499    9.308047551          37.22290          9.069195        46.29210
## 500   -4.007434151          50.41320         10.400743        60.81394
## 501   58.661797284          24.93143         53.464719        78.39615
## 502   48.935653346          22.62581         49.574261        72.20007
## 503   11.175551186          33.32413         34.470220        67.79435
## 504   46.491174104          26.95106         48.596470        75.54753
## 505   50.407211070          24.51392         50.162884        74.67680
## 506   54.446202514          16.89160         51.778481        68.67008
## 507   16.308191288          38.01703         36.523277        74.54031
## 508   -7.133527067          48.78162         27.146589        75.92821
## 509   55.614122765          20.93016         52.245649        73.17581
## 510   57.669875096          28.30307         53.067950        81.37102
## 511   30.485108725          42.10018         42.194043        84.29422
## 512    5.368114959          48.93142         32.147246        81.07866
## 513    1.397049229          41.47497         30.558820        72.03379
## 514   -2.452633490          48.24794         29.018947        77.26688
## 515    1.248887437          52.45056         30.499555        82.95012
## 516    8.290664740          33.61464         33.316266        66.93091
## 517   21.077678518          34.46845         38.431071        72.89952
## 518   -7.444312288          41.14573         27.022275        68.16801
## 519   -9.220320259          47.73871         26.311872        74.05058
## 520    3.212430845          50.08806         31.284972        81.37303
## 521   18.719644034          38.85150         37.487858        76.33936
## 522   11.731418525          27.71370         34.692567        62.40627
## 523   38.550828840          25.83770         45.420332        71.25803
## 524   29.132819278          41.07451         41.653128        82.72763
## 525   24.944225498          28.70902         39.977690        68.68671
## 526   21.600962784          41.00772         38.640385        79.64811
## 527   40.379835151          31.36150         46.151934        77.51343
## 528   -3.712113444          50.83901         28.515155        79.35417
## 529   52.055592178          27.02502         50.822237        77.84726
## 530   31.884317696          38.65337         42.753727        81.40710
## 531   37.637846440          23.12301         45.055139        68.17815
## 532   12.614593883          38.89561         35.045838        73.94145
## 533   33.368961038          33.40685         43.347584        76.75443
## 534    0.773476805          39.47848         30.309391        69.78787
## 535   -1.819989877          47.01553         29.272004        76.28753
## 536   11.242112599          43.34820         34.496845        77.84504
## 537   47.156660045          32.60230         48.862664        81.46497
## 538   14.673160790          45.88870         35.869264        81.75797
## 539   16.736138479          38.53831         36.694455        75.23277
## 540   12.914373537          42.32674         35.165749        77.49249
## 541   54.511243994          21.16167         51.804498        72.96617
## 542   55.708895533          21.02686         52.283558        73.31042
## 543   18.471409497          39.06232         37.388564        76.45089
## 544   53.102590395          28.55204         51.241036        79.79308
## 545   38.772379842          23.84422         45.508952        69.35317
## 546   -9.636993143          46.87989         26.145203        73.02509
## 547    3.418869474          39.97975         31.367548        71.34730
## 548   26.325047668          37.32374         40.530019        77.85376
## 549   10.485312976          28.07295         34.194125        62.26708
## 550   46.280103151          25.78180         48.512041        74.29384
## 551   -9.834403773          43.60390         26.066238        69.67014
## 552   29.532524408          34.09584         41.813010        75.90884
## 553   -6.713796814          45.94950         27.314481        73.26398
## 554    5.309751546          49.69913         32.123901        81.82303
## 555   46.169148411          12.30580         48.467659        60.77346
## 556   18.630159721          35.82025         37.452064        73.27232
## 557    0.083816657          44.70944         30.033527        74.74297
## 558   -8.582542338          46.63057         26.566983        73.19755
## 559   39.502404546          28.09194         45.800962        73.89290
## 560   -1.619414131          35.93230         29.352234        65.28454
## 561   41.007277179          24.55245         46.402911        70.95536
## 562   34.429928167          26.41897         43.771971        70.19094
## 563   38.736602822          36.17756         45.494641        81.67220
## 564   21.500695178          25.26026         38.600278        63.86053
## 565   40.602626051          31.79247         46.241050        78.03352
## 566    1.524338606          42.78509         30.609735        73.39483
## 567   14.762168399          24.91393         35.904867        60.81879
## 568    2.822578254          43.74822         31.129031        74.87725
## 569   15.798200881          27.84152         36.319280        64.16080
## 570   18.196282743          36.45712         37.278513        73.73563
## 571   26.648840308          39.35864         40.659536        80.01818
## 572    2.987900379          35.02644         31.195160        66.22160
## 573   16.873922981          29.01098         36.749569        65.76055
## 574    2.693965614          38.40753         31.077586        69.48512
## 575   58.660954328          12.34555         53.464382        65.80993
## 576   -0.501249330          40.47497         29.799500        70.27447
## 577   41.602464574          26.59780         46.640986        73.23879
## 578   14.297821631          40.22797         35.719129        75.94710
## 579   33.996972230          26.91412         43.598789        70.51291
## 580   30.148334401          33.72075         42.059334        75.78009
## 581   16.829769204          45.65916         36.731908        82.39106
## 582   13.809373053          43.11052         35.523749        78.63427
## 583   37.427728896          24.50968         44.971092        69.48077
## 584   35.233973456          39.09055         44.093589        83.18414
## 585   54.669967440          25.04378         51.867987        76.91177
## 586    0.512135918          43.45491         30.204854        73.65977
## 587   55.606643024          21.30211         52.242657        73.54477
## 588   -2.999313027          40.51799         28.800275        69.31826
## 589   59.136883975          16.94291         53.654754        70.59767
## 590   44.816066173          31.71063         47.926426        79.63706
## 591   30.100453368          33.00496         42.040181        75.04514
## 592   32.665909030          19.22899         43.066364        62.29535
## 593   52.993560710          12.94425         51.197424        64.14168
## 594    7.210964882          40.62843         32.884386        73.51282
## 595   31.728462903          38.74882         42.691385        81.44020
## 596   31.619454715          27.24640         42.647782        69.89418
## 597   -5.149374004          40.80892         27.940250        68.74917
## 598   52.761712475          17.50166         51.104685        68.60634
## 599   35.666869220          32.19212         44.266748        76.45886
## 600   51.558369754          31.24599         50.623348        81.86934
## 601   42.947229478          30.59874         47.178892        77.77763
## 602   38.788304776          38.63170         45.515322        84.14703
## 603   46.378857833          23.04102         48.551543        71.59257
## 604   -1.884159015          37.58336         29.246336        66.82970
## 605   45.814584694          27.44617         48.325834        75.77201
## 606   38.802756912          23.11316         45.521103        68.63426
## 607   54.312322396          26.21605         51.724929        77.94098
## 608   30.478900305          26.54977         42.191560        68.74133
## 609   14.792922933          33.47151         35.917169        69.38868
## 610   24.806741241          34.16181         39.922696        74.08451
## 611   49.109024098          20.09372         49.643610        69.73733
## 612   58.398802935          24.90971         53.359521        78.26924
## 613   21.754505604          32.69491         38.701802        71.39671
## 614   58.100387729          16.22376         53.240155        69.46392
## 615    9.937807792          37.60154         33.975123        71.57666
## 616   19.675829231          44.16649         37.870332        82.03682
## 617   -3.010980054          45.95760         28.795608        74.75321
## 618   26.277591251          38.79718         40.511037        79.30821
## 619   29.273589340          24.24476         41.709436        65.95420
## 620   13.316957082          42.07039         35.326783        77.39717
## 621   30.704852182          36.58594         42.281941        78.86788
## 622    9.639261484          44.81286         33.855705        78.66857
## 623   -9.997234889          50.80008         26.001106        76.80119
## 624   47.001125657          29.56438         48.800450        78.36483
## 625   35.697940607          30.27002         44.279176        74.54919
## 626   -2.261464919          40.15841         29.095414        69.25382
## 627   16.291107198          45.37107         36.516443        81.88751
## 628    6.853332534          39.36540         32.741333        72.10674
## 629   47.469218487          23.18211         48.987687        72.16980
## 630   -1.135978259          39.20553         29.545609        68.75114
## 631   32.497499760          28.68594         42.999000        71.68494
## 632   50.543975618          22.10697         50.217590        72.32456
## 633   55.118968005          28.15158         52.047587        80.19917
## 634   54.370021953          17.77473         51.748009        69.52274
## 635   43.442608712          28.38762         47.377043        75.76466
## 636   21.359380661          30.43608         38.543752        68.97984
## 637   30.944686835          32.93526         42.377875        75.31313
## 638   18.446887520          34.51004         37.378755        71.88879
## 639    3.606899234          45.41653         31.442760        76.85929
## 640   -1.010072529          41.68920         29.595971        71.28517
## 641    1.372325644          43.67097         30.548930        74.21990
## 642   27.750192774          31.37310         41.100077        72.47318
## 643   52.415315220          29.98001         50.966126        80.94613
## 644    0.938489884          42.93473         30.375396        73.31012
## 645   17.833936401          39.63269         37.133575        76.76626
## 646   25.534658872          44.09555         40.213864        84.30941
## 647   44.924682993          33.94355         47.969873        81.91342
## 648   50.517470906          34.27732         50.206988        84.48430
## 649   -2.941358192          51.98907         28.823457        80.81252
## 650   -5.693742121          42.91663         27.722503        70.63913
## 651    8.565475098          39.49163         33.426190        72.91782
## 652   25.525712690          40.53423         40.210285        80.74451
## 653   37.185053395          28.17412         44.874021        73.04814
## 654   49.375076289          23.96214         49.750031        73.71217
## 655   10.520821614          37.05466         34.208329        71.26299
## 656   18.853312277          38.05199         37.541325        75.59332
## 657   24.611897911          32.23065         39.844759        72.07541
## 658   36.671110850          35.42186         44.668444        80.09031
## 659   50.046745078          19.02965         50.018698        69.04834
## 660   12.292874644          34.68331         34.917150        69.60046
## 661   54.709568641          28.29194         51.883827        80.17577
## 662   55.227787003          26.83073         52.091115        78.92184
## 663   52.866844686          18.56127         51.146738        69.70801
## 664   37.673345446          24.52643         45.069338        69.59577
## 665   -3.596650702          49.68448         28.561340        78.24582
## 666   13.175868702          33.72855         35.270347        68.99890
## 667   42.324181951          27.19771         46.929673        74.12738
## 668   27.595990677          32.91300         41.038396        73.95140
## 669   43.723294241          36.97170         47.489318        84.46102
## 670   13.575731695          41.63342         35.430293        77.06371
## 671   32.182215697          38.28553         42.872886        81.15841
## 672   54.836292814          19.76011         51.934517        71.69463
## 673   36.817849716          22.89089         44.727140        67.61803
## 674   41.718387560          25.99935         46.687355        72.68671
## 675    9.973385176          37.01484         33.989354        71.00419
## 676   -4.616710090          38.02256         28.153316        66.17587
## 677   28.553590211          36.15000         41.421436        77.57144
## 678   20.040461731          31.55566         38.016185        69.57184
## 679    6.781046691          44.12252         32.712419        76.83494
## 680   26.737952747          33.07791         40.695181        73.77309
## 681   -7.086414476          36.64969         27.165434        63.81512
## 682   10.646816201          32.42951         34.258726        66.68823
## 683    0.744075261          49.51618         30.297630        79.81381
## 684   54.656878677          23.01596         51.862751        74.87872
## 685   -4.362420433          43.58993         28.255032        71.84497
## 686   59.536681792          19.83731         53.814673        73.65198
## 687   -9.130863179          41.31993         26.347655        67.66758
## 688    2.654891952          47.34865         31.061957        78.41060
## 689   55.842467209          29.47370         52.336987        81.81069
## 690    2.612206915          51.02606         31.044883        82.07094
## 691   41.903881931          19.67201         46.761553        66.43356
## 692   24.172291777          30.90924         39.668917        70.57815
## 693   17.119122364          41.66605         36.847649        78.51370
## 694   -9.500753460          38.25314         26.199699        64.45284
## 695   39.089961341          23.03467         45.635985        68.67065
## 696   46.033077708          25.27286         48.413231        73.68609
## 697   -0.004846442          47.43831         29.998061        77.43637
## 698   50.860603268          22.62727         50.344241        72.97151
## 699   21.740058619          44.20305         38.696023        82.89908
## 700   27.766389642          32.71639         41.106556        73.82294
## 701    5.849816839          38.40919         32.339927        70.74911
## 702   23.599626787          35.45660         39.439851        74.89645
## 703   -3.234379755          47.24264         28.706248        75.94889
## 704    7.267164765          41.58779         32.906866        74.49465
## 705   58.686222353          21.73985         53.474489        75.21434
## 706    3.615782831          41.07679         31.446313        72.52310
## 707   54.184220165          18.27865         51.673688        69.95234
## 708   43.161858544          25.90424         47.264743        73.16899
## 709   -9.105166220          44.76545         26.357934        71.12338
## 710   32.887274087          36.07607         43.154910        79.23098
## 711   20.442302309          37.23670         38.176921        75.41362
## 712   30.150400843          33.11442         42.060160        75.17459
## 713   30.453063899          37.06513         42.181226        79.24636
## 714   45.422344408          25.64732         48.168938        73.81626
## 715   29.685309625          30.16744         41.874124        72.04156
## 716   -8.126900296          61.22303         26.749240        87.97227
## 717   22.213790868          31.43895         38.885516        70.32447
## 718   43.081677423          16.40036         47.232671        63.63303
## 719   23.801510525          28.84441         39.520604        68.36502
## 720   49.333990670          15.16344         49.733596        64.89704
## 721   50.663627586          27.00120         50.265451        77.26665
## 722   -1.818223565          50.41282         29.272711        79.68553
## 723   16.423462625          44.21537         36.569385        80.78475
## 724   47.255869608          24.23488         48.902348        73.13723
## 725   43.120180976          30.38693         47.248072        77.63501
## 726   48.849958873          23.54251         49.539984        73.08250
## 727   27.417121290          35.38399         40.966849        76.35084
## 728   56.596933573          19.76147         52.638773        72.40024
## 729   22.560676057          34.01056         39.024270        73.03483
## 730   44.169791965          28.65278         47.667917        76.32070
## 731    4.238312989          37.26513         31.695325        68.96045
## 732   -5.199106897          45.65226         27.920357        73.57261
## 733    6.014335400          49.88725         32.405734        82.29298
## 734   -5.393109096          39.21596         27.842756        67.05872
## 735   -0.190447501          34.28567         29.923821        64.20949
## 736   25.824367430          31.61519         40.329747        71.94493
## 737   -5.480912516          45.41860         27.807635        73.22624
## 738   26.768135754          27.13289         40.707254        67.84014
## 739   55.124538760          27.54115         52.049816        79.59097
## 740   41.983816917          18.70567         46.793527        65.49920
## 741   40.430146791          23.83582         46.172059        70.00788
## 742   11.543229646          42.07820         34.617292        76.69550
## 743   23.344603779          39.97884         39.337842        79.31668
## 744   47.801610208          35.62204         49.120644        84.74268
## 745   48.432942538          20.03569         49.373177        69.40887
## 746    6.263462375          38.71452         32.505385        71.21991
## 747   29.852761363          26.80130         41.941105        68.74240
## 748   37.933199403          19.44687         45.173280        64.62014
## 749    7.295352716          40.77252         32.918141        73.69066
## 750   13.801330603          41.12838         35.520532        76.64892
## 751   20.359139182          46.69470         38.143656        84.83836
## 752   20.540781307          41.67626         38.216313        79.89257
## 753   57.186875020          22.71430         52.874750        75.58905
## 754   59.817361340          28.15108         53.926945        82.07802
## 755   -7.717159127          45.32616         26.913136        72.23930
## 756   32.911955819          27.24689         43.164782        70.41167
## 757   42.000486008          34.77465         46.800194        81.57485
## 758   -4.360336715          43.73523         28.255865        71.99110
## 759   -2.042368646          46.00662         29.183053        75.18967
## 760   22.240042503          43.88763         38.896017        82.78365
## 761    0.078375342          43.18015         30.031350        73.21150
## 762   29.185384512          42.66579         41.674154        84.33994
## 763    8.177388182          41.96065         33.270955        75.23161
## 764   45.126663966          14.05734         48.050666        62.10801
## 765   46.540126496          28.13800         48.616051        76.75405
## 766   31.165217231          32.67398         42.466087        75.14006
## 767   58.719370710          13.61270         53.487748        67.10044
## 768   48.729162384          17.39964         49.491665        66.89131
## 769    9.040006869          38.33379         33.616003        71.94979
## 770   49.753134190          28.92910         49.901254        78.83035
## 771    3.110962033          42.41768         31.244385        73.66207
## 772   51.522445448          25.58867         50.608978        76.19765
## 773   46.428897718          29.46489         48.571559        78.03645
## 774   -2.325825333          47.28093         29.069670        76.35060
## 775   53.906231963          21.14608         51.562493        72.70857
## 776   44.187532039          23.18860         47.675013        70.86362
## 777   10.039842247          42.81276         34.015937        76.82870
## 778   30.829978127          34.19066         42.331991        76.52265
## 779   19.890107301          37.37220         37.956043        75.32825
## 780   36.941563801          22.56832         44.776626        67.34494
## 781   14.489336554          29.78114         35.795735        65.57688
## 782    2.418134015          47.06325         30.967254        78.03051
## 783   29.822278421          44.50452         41.928911        86.43343
## 784   43.437362127          21.58854         47.374945        68.96348
## 785   -5.301772824          39.80702         27.879291        67.68631
## 786    5.460497751          42.41535         32.184199        74.59955
## 787   44.912206372          25.33359         47.964883        73.29847
## 788   47.464612501          22.02959         48.985845        71.01543
## 789   20.016756144          25.71249         38.006702        63.71919
## 790   56.285124747          27.69978         52.514050        80.21383
## 791   14.925605822          45.78110         35.970242        81.75134
## 792   20.505292749          40.37591         38.202117        78.57802
## 793    4.947609811          41.33912         31.979044        73.31817
## 794   19.449873378          29.38068         37.779949        67.16063
## 795   47.519067293          28.45025         49.007627        77.45788
## 796   49.352313746          28.38465         49.740925        78.12558
## 797   31.510620592          30.23849         42.604248        72.84274
## 798    1.188903076          45.91098         30.475561        76.38655
## 799   47.207768729          25.63481         48.883107        74.51792
## 800   41.790700310          30.28241         46.716280        76.99869
## 801   20.198292152          43.48737         38.079317        81.56669
## 802   -6.237917040          40.82539         27.504833        68.33022
## 803   17.878792400          25.50192         37.151517        62.65344
## 804   22.747236425          29.17459         39.098895        68.27348
## 805   55.372039734          16.85748         52.148816        69.00629
## 806   25.704138882          34.81373         40.281656        75.09539
## 807   24.835474773          34.89243         39.934190        74.82662
## 808   41.264852770          33.91429         46.505941        80.42023
## 809   49.388248157          21.77489         49.755299        71.53019
## 810   27.528446650          21.78209         41.011379        62.79346
## 811   26.376340049          29.75094         40.550536        70.30148
## 812   51.451111287          31.62855         50.580445        82.20899
## 813    4.010260755          42.70379         31.604104        74.30789
## 814   20.168127171          42.81898         38.067251        80.88623
## 815   28.785664372          25.39251         41.514266        66.90677
## 816   39.646026327          33.27215         45.858411        79.13056
## 817   -1.936236657          56.55699         29.225505        85.78249
## 818   29.393150837          27.07302         41.757260        68.83028
## 819   39.532037980          35.76467         45.812815        81.57748
## 820   -8.399492786          38.29439         26.640203        64.93459
## 821   56.199856601          22.90764         52.479943        75.38758
## 822   51.237123895          30.47954         50.494850        80.97439
## 823    3.292536326          54.61037         31.317015        85.92739
## 824   23.048459394          29.97990         39.219384        69.19929
## 825   -1.594924587          53.59131         29.362030        82.95334
## 826   39.015396284          36.45239         45.606159        82.05855
## 827   21.742119323          33.41818         38.696848        72.11503
## 828   58.457655944          14.38088         53.383062        67.76395
## 829   11.036096776          36.15162         34.414439        70.56606
## 830    7.677470632          41.50243         33.070988        74.57342
## 831   12.537970925          36.28324         35.015188        71.29843
## 832   45.791800881          33.18556         48.316720        81.50228
## 833   31.274811842          23.81431         42.509925        66.32424
## 834   -4.810828967          40.59460         28.075668        68.67026
## 835   -4.870159186          44.77749         28.051936        72.82943
## 836   17.353010948          25.70247         36.941204        62.64367
## 837   28.143752753          33.85536         41.257501        75.11286
## 838    6.578480974          35.38117         32.631392        68.01256
## 839    1.419335264          34.08433         30.567734        64.65206
## 840   22.711663784          38.32220         39.084666        77.40687
## 841   19.166167101          38.37906         37.666467        76.04553
## 842    8.774300378          30.08778         33.509720        63.59750
## 843   16.543802505          35.99184         36.617521        72.60936
## 844   42.225335625          24.07780         46.890134        70.96793
## 845   44.247586955          33.11273         47.699035        80.81177
## 846   37.243342733          29.77099         44.897337        74.66832
## 847   -2.522874991          46.90953         28.990850        75.90038
## 848    9.202862841          42.22814         33.681145        75.90929
## 849   21.483835594          34.64702         38.593534        73.24055
## 850   35.070311704          30.74158         44.028125        74.76971
## 851   26.998093699          31.05159         40.799237        71.85083
## 852    4.559644365          37.19127         31.823858        69.01513
## 853   24.361840377          33.53377         39.744736        73.27851
## 854   23.952250781          27.32630         39.580900        66.90720
## 855   22.555263736          35.71174         39.022105        74.73385
## 856   51.876789434          27.74447         50.750716        78.49519
## 857   49.164543126          21.98091         49.665817        71.64672
## 858   -4.517888797          57.59268         28.192844        85.78553
## 859   53.130177010          24.58548         51.252071        75.83755
## 860   42.945878231          24.71737         47.178351        71.89573
## 861   29.796112238          25.15077         41.918445        67.06921
## 862   58.812179519          13.29216         53.524872        66.81703
## 863   32.539413699          32.01752         43.015765        75.03329
## 864    4.324674252          39.73079         31.729870        71.46066
## 865   15.610495193          30.10028         36.244198        66.34447
## 866    4.251844753          54.49601         31.700738        86.19674
## 867   -8.835178108          43.58610         26.465929        70.05202
## 868   31.626613871          39.93293         42.650646        82.58358
## 869   47.929627949          26.36069         49.171851        75.53254
## 870   49.962843254          31.71048         49.985137        81.69562
## 871   34.542141238          29.05739         43.816856        72.87425
## 872   31.121901569          32.08879         42.448761        74.53755
## 873   51.673862729          23.51561         50.669545        74.18516
## 874    8.099576111          45.13238         33.239830        78.37221
## 875   52.620519476          25.55459         51.048208        76.60279
## 876    1.283623918          47.59319         30.513450        78.10664
## 877   14.015075723          30.98529         35.606030        66.59132
## 878   13.836401831          47.35237         35.534561        82.88693
## 879   25.070618999          37.79252         40.028248        77.82076
## 880    4.755247042          44.74703         31.902099        76.64913
## 881    7.218235908          35.48252         32.887294        68.36981
## 882   -3.530001687          45.43351         28.587999        74.02151
## 883   22.191097673          29.46989         38.876439        68.34633
## 884   26.650965163          39.47770         40.660386        80.13808
## 885    0.297888799          36.21062         30.119156        66.32978
## 886   14.788766678          50.16683         35.915507        86.08234
## 887   50.078875893          18.27409         50.031550        68.30565
## 888   48.587831911          21.07189         49.435133        70.50702
## 889   -6.595486852          41.54832         27.361805        68.91012
## 890   12.415291853          43.75387         34.966117        78.71998
## 891   34.298637498          31.98895         43.719455        75.70841
## 892   -0.275156084          54.05384         29.889938        83.94378
## 893    1.536679855          44.12599         30.614672        74.74067
## 894   37.246204410          22.09232         44.898482        66.99080
## 895   50.340816258          13.12098         50.136327        63.25731
## 896    3.530969843          45.72760         31.412388        77.13999
## 897   -4.581355567          45.70641         28.167458        73.87386
## 898   34.288542215          37.40438         43.715417        81.11979
## 899   20.216350139          36.34726         38.086540        74.43380
## 900   30.833109359          34.30278         42.333244        76.63602
## 901   44.413334690          14.08231         47.765334        61.84764
## 902   41.467110012          37.35504         46.586844        83.94188
## 903   28.812145728          24.76617         41.524858        66.29103
## 904   -5.968423348          51.53830         27.612631        79.15093
## 905   16.997654978          34.78716         36.799062        71.58622
## 906   51.386943648          31.38690         50.554777        81.94167
## 907   21.271848832          43.58203         38.508740        82.09077
## 908   43.176320344          17.50175         47.270528        64.77228
## 909   18.939912471          21.74969         37.575965        59.32565
## 910   40.677542593          21.43413         46.271017        67.70515
## 911    0.115846097          47.76271         30.046338        77.80905
## 912   46.448879195          24.58812         48.579552        73.16767
## 913   40.043594786          27.90682         46.017438        73.92426
## 914   10.962558812          40.95274         34.385024        75.33777
## 915   -6.788334555          40.62554         27.284666        67.91020
## 916   52.561174328          21.63344         51.024470        72.65791
## 917   59.872334201          17.72712         53.948934        71.67605
## 918   23.752204676          24.21693         39.500882        63.71781
## 919    0.884615812          42.59021         30.353846        72.94405
## 920   13.874710409          39.65640         35.549884        75.20629
## 921   40.970236841          22.82050         46.388095        69.20859
## 922   59.714630400          25.69223         53.885852        79.57808
## 923   13.033175785          35.63409         35.213270        70.84736
## 924   53.806639034          23.95460         51.522656        75.47726
## 925    7.892646305          43.66273         33.157059        76.81979
## 926   45.283657918          25.85104         48.113463        73.96450
## 927    6.384794959          43.90833         32.553918        76.46225
## 928   10.559404963          29.94043         34.223762        64.16420
## 929   38.918110831          23.30530         45.567244        68.87255
## 930   28.500437071          37.61805         41.400175        79.01822
## 931    8.912190818          53.14492         33.564876        86.70979
## 932   50.665318943          28.71903         50.266128        78.98516
## 933    3.756918737          47.20367         31.502767        78.70644
## 934   -1.198237271          40.71026         29.520705        70.23096
## 935   59.425098873          20.02778         53.770040        73.79782
## 936   22.673792730          35.33238         39.069517        74.40190
## 937   25.674071363          30.53549         40.269629        70.80512
## 938    9.142799091          46.50961         33.657120        80.16673
## 939   -2.346206799          44.84217         29.061517        73.90368
## 940    2.062083972          44.89179         30.824834        75.71662
## 941    4.533684549          40.93883         31.813474        72.75230
## 942   21.365852051          43.04796         38.546341        81.59430
## 943   50.216303042          18.38068         50.086521        68.46720
## 944   28.756729313          32.40840         41.502692        73.91109
## 945   24.397745451          38.24761         39.759098        78.00671
## 946   10.058995502          45.53364         34.023598        79.55723
## 947    2.503838919          45.74299         31.001536        76.74453
## 948    5.375193765          48.35207         32.150078        80.50215
## 949   -4.866806804          53.33632         28.053277        81.38960
## 950   14.590581348          39.78180         35.836233        75.61803
## 951    4.388284951          41.74764         31.755314        73.50295
## 952    5.934556942          41.72808         32.373823        74.10190
## 953   57.283392961          21.21697         52.913357        74.13033
## 954   58.921540072          18.11306         53.568616        71.68168
## 955   13.945402424          44.09885         35.578161        79.67702
## 956   56.349351874          21.13375         52.539741        73.67349
## 957    0.637215364          43.38039         30.254886        73.63527
## 958   18.978624200          29.13427         37.591450        66.72572
## 959   34.495270152          35.59658         43.798108        79.39469
## 960    6.579339593          39.89921         32.631736        72.53094
## 961    2.116218146          40.66167         30.846487        71.50816
## 962    4.264002484          49.66727         31.705601        81.37287
## 963   13.643642447          34.93970         35.457457        70.39715
## 964   39.417175516          29.55686         45.766870        75.32373
## 965   -4.877937492          56.27135         28.048825        84.32018
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## 999          TRUE        FALSE
## 1000         TRUE        FALSE

2SLS

We could manually run the first stage model, generate predicted tutoring and then use those predicted values in the second stage model like we did in the instrumental variables example, but that’s tedious and nobody wants to do all that work. We’ll use iv_robust() from the estimatr package instead.

Note: be careful! if there are missing values (in D), you may fail to replicate the fuzzy effect by hand sum(is.na(crab_data$fished)) #ok for the simulated data

Instead, we need to run a 2SLS model that includes our instrument in the first stage, which will then remove the endogeneity built into participation in the program. We’ll estimate this set of models:

##NEED TO FINISHED - IS THIS RIGHT??? \[ \begin{aligned} \widehat{\text{Fished}} &= \gamma_0 + \gamma_1 \text{Size}_\text{centered} + \gamma_2 \text{Below cutoff} + \omega \\ \text{Fishing Mortality} &= \beta_0 + \beta_1 \text{Size}_\text{centered} + \beta_2 \widehat{\text{Fished}} + \epsilon \end{aligned} \]

Fuzzy nonparametric estimation

We can also use nonparametric methods to measure the size of the fuzzy gap at the cutoff. We’ll use rdrobust(). T

To do fuzzy estimation with rdrobust(), use the fuzzy argument to specify the treatment column (or fished in our case). Importantly (and confusingly! this took me waaaaay too long to figure out!), you do not need to specify an instrument (or even create one!). All you need to specify is the column that indicates treatment status—rdrobust() will do all the above/below-the-cutoff instrument stuff behind the scenes for you.

##NEED TO FINISHED WITH IV CREATED AS ENTRANCE EXAM

rdrobust(y = crab_data$fishing_mortality, x = crab_data$size_centered,
         c = 0, fuzzy = crab_data$fished) %>%
  summary()

## Fuzzy RD estimates using local polynomial regression.
## 
## Number of Obs.                 1000
## BW type                       mserd
## Kernel                   Triangular
## VCE method                       NN
## 
## Number of Obs.                  481          519
## Eff. Number of Obs.             170          207
## Order est. (p)                    1            1
## Order bias  (q)                   2            2
## BW est. (h)                  15.916       15.916
## BW bias (b)                  27.226       27.226
## rho (h/b)                     0.585        0.585
## Unique Obs.                     481          519
## 
## First-stage estimates.
## 
## =============================================================================
##         Method     Coef. Std. Err.         z     P>|z|      [ 95% C.I. ]       
## =============================================================================
##   Conventional    -0.055     0.102    -0.538     0.591    [-0.254 , 0.145]     
##         Robust         -         -    -0.208     0.835    [-0.257 , 0.207]     
## =============================================================================
## 
## Treatment effect estimates.
## 
## =============================================================================
##         Method     Coef. Std. Err.         z     P>|z|      [ 95% C.I. ]       
## =============================================================================
##   Conventional    16.226     7.058     2.299     0.022     [2.392 , 30.060]    
##         Robust         -         -     1.453     0.146    [-4.192 , 28.216]    
## =============================================================================

That’s all! Using nonparametric methods, with a triangular kernel and a bandwidth of ±12.96, the causal effect of the tutoring program for compliers in the bandwidth is 9.683.

We can (and should!) do all the other nonparametric robustness checks that we talked about in the regression discontinuity example, like modifying the bandwidth (ideal, half, double) and messing with the kernel (uniform, triangular, Epanechnikov) to see how robust the finding is. But again, we won’t do any of that here.

Useful references and websites for more resources

https://dimewiki.worldbank.org/Regression_Discontinuity

the MixTape by Scott Cummingham: https://mixtape.scunning.com/06-regression_discontinuity

RDD with interactions: https://www.jepusto.com/rdd-interactions/

Simulate Data

Modified from the MixTape by Scott Cummingham: https://mixtape.scunning.com/06-regression_discontinuity

library(tidyverse)
# simulate the data
dat <- tibble(
  x = rnorm(1000, 50, 25)
) %>%
  mutate(
    x = if_else(x < 0, 0, x)
  ) %>%
  filter(x < 100)

# cutoff at x = 70, no jump
dat <- dat %>% 
  mutate(
    D  = if_else(x > 70, 1, 0),
    y1 = 25 + 0 * D + 1.5 * x + rnorm(n(), 0, 20)
  )

ggplot(aes(x, y1, colour = factor(D)), data = dat) +
  geom_point(alpha = 0.5) +
  geom_vline(xintercept = 70, colour = "grey", linetype = 2)+
  stat_smooth(method = "lm", se = F) +
  labs(x = "Test score (X)", y = "Potential Outcome (Y1)")

## `geom_smooth()` using formula = 'y ~ x'

## simulate the discontinuity
dat <- dat %>%
  mutate(
    y2 = 25 + 40 * D + 1.5 * x + rnorm(n(), 0, 20)
  )

# figure
ggplot(aes(x, y2, colour = factor(D)), data = dat) +
  geom_point(alpha = 0.5) +
  geom_vline(xintercept = 70, colour = "grey", linetype = 2) +
  stat_smooth(method = "lm", se = F) +
  labs(x = "Test score (X)", y = "Potential Outcome (Y)")

## `geom_smooth()` using formula = 'y ~ x'

# simultate nonlinearity
dat <- tibble(
    x = rnorm(1000, 100, 50)
  ) %>% 
  mutate(
    x = case_when(x < 0 ~ 0, TRUE ~ x),
    D = case_when(x > 140 ~ 1, TRUE ~ 0),
    x2 = x*x,
    x3 = x*x*x,
    y3 = 10000 + 0 * D - 100 * x + x2 + rnorm(1000, 0, 1000)
  ) %>% 
  filter(x < 280)

ggplot(aes(x, y3, colour = factor(D)), data = dat) +
  geom_point(alpha = 0.2) +
  geom_vline(xintercept = 140, colour = "grey", linetype = 2) +
  stat_smooth(method = "lm", se = F) +
  labs(x = "Test score (X)", y = "Potential Outcome (Y)")

## `geom_smooth()` using formula = 'y ~ x'

ggplot(aes(x, y3, colour = factor(D)), data = dat) +
  geom_point(alpha = 0.2) +
  geom_vline(xintercept = 140, colour = "grey", linetype = 2) +
  stat_smooth(method = "loess", se = F) +
  labs(x = "Test score (X)", y = "Potential Outcome (Y)")

## `geom_smooth()` using formula = 'y ~ x'

–>

We can check the size two different ways: parametrically (i.e. using lm() with specific parameters and coefficients), and nonparametrically (i.e. not using lm() or any kind of straight line and instead drawing lines that fit the data more precisely). We’ll do it both ways.

Parametric estimation

First we’ll do it parametrically by using linear regression. Here we want to explain the variation in final scores based on the entrance exam score and participation in the tutoring program:

\[ \text{Exit exam} = \beta_0 + \beta_1 \text{Entrance exam score}_\text{centered} + \beta_2 \text{Tutoring program} + \epsilon \]

Nonparametric estimation

Instead of using linear regression to measure the size of the discontinuity, we can use nonparametric methods. Essentially this means that R will not try to fit a straight line to the data—instead it’ll curve around the points and try to fit everything as smoothly as possible.

The rdrobust() function makes it really easy to measure the gap at the cutoff with nonparametric estimation. Here’s the simplest version: